Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
51201	Find the Average Rate of Change	S(t)=155(7-7/(6+t))	$S (t) = 155 (7 - \frac{7}{6 + t})$
51202	Find the Average Rate of Change	table[[x,y],[-1,8/3],[0,2],[1,3/2]]	$\begin{array}{c} x & y \\ - 1 & \frac{8}{3} \\ 0 & 2 \\ 1 & \frac{3}{2} \end{array}$
51203	Find the Average Rate of Change	3/4	$\frac{3}{4}$
51204	Find the Average Rate of Change	f(x)=-2x^3+7x^2+x	$f (x) = - 2 x^{3} + 7 x^{2} + x$
51205	Find the Average Rate of Change	f(x)=(x+3)(x-3)	$f (x) = (x + 3) (x - 3)$
51206	Find the Average Rate of Change	A=1100(1+i)^3	$A = 1100 {(1 + i)}^{3}$
51207	Find the Average Rate of Change	y = log base 1/2 of x	$y = \log_{\frac{1}{2}} (x)$
51208	Find the Average Rate of Change	table[[x,h(x)],[0,10],[1,4]]	$\begin{array}{c} x & h (x) \\ 0 & 10 \\ 1 & 4 \end{array}$
51209	Find the Average Rate of Change	table[[x,y],[-1,1/25],[0,1/5],[1,1],[2,5]]	$\begin{array}{c} x & y \\ - 1 & \frac{1}{25} \\ 0 & \frac{1}{5} \\ 1 & 1 \\ 2 & 5 \end{array}$
51210	Find the Average Rate of Change	f(t)=4(1.25)^(t+3)	$f (t) = 4 {(1.25)}^{t + 3}$
51211	Find the Average Rate of Change	b(t)=4(2)^t	$b (t) = 4 {(2)}^{t}$
51212	Find the Average Rate of Change	What is the average rate of change of h(x)=1/(10-x) over the interval 5<=x<=8 ?	What is the average rate of change of $h (x) = \frac{1}{10 - x}$ over the interval $5 \leq x \leq 8$ ?
51213	Find the Average Rate of Change	h(x)=1/8x^3-x^2 , -2<=x<=2	$h (x) = \frac{1}{8} x^{3} - x^{2}$ , $- 2 \leq x \leq 2$
51214	Find the Average Rate of Change	f(x)=1/( square root of x) on 1 , 9	$f (x) = \frac{1}{\sqrt{x}}$ on $1$ , $9$
51215	Find the Average Rate of Change	g(x)=9x^3-8 on -3 , 3	$g (x) = 9 x^{3} - 8$ on $- 3$ , $3$
51216	Find the Average Rate of Change	x^3+x^2-8x-7	$x^{3} + x^{2} - 8 x - 7$
51217	Find the Average Rate of Change	T(x)=x^3(7-x^2)+98.6	$T (x) = x^{3} (7 - x^{2}) + 98.6$
51218	Find the Average Rate of Change	f(x)=sin(x) , [0,pi]	$f (x) = \sin (x)$ , $[0, π]$
51219	Find the Average Rate of Change	4(0.8)^t	$4 {(0.8)}^{t}$
51220	Find the Average Rate of Change	h(x)=x^2-1 , -3<=x<=-1	$h (x) = x^{2} - 1$ , $- 3 \leq x \leq - 1$
51221	Find the Average Rate of Change	F(x)=-x^3+3x , [-2,-1]	$F (x) = - x^{3} + 3 x$ , $[- 2, - 1]$
51222	Find the Average Rate of Change	f(x)=x^2+5x+6 on 2 , 2.01	$f (x) = x^{2} + 5 x + 6$ on $2$ , $2.01$
51223	Find the Average Rate of Change	f(x)=(\|\|x\|\|+2)/2 , if 0<=x<6	$f (x) = \frac{\| \| x \| \| + 2}{2}$ , if $0 \leq x < 6$
51224	Find the Average Rate of Change	p(t)=500*2t	$p (t) = 500 \cdot 2 t$
51225	Find the Average Rate of Change	h(x)=1/8x^3-x^2 -2<=x<=2	$h (x) = \frac{1}{8} x^{3} - x^{2}$ $- 2 \leq x \leq 2$
51226	Find the Average Rate of Change	f(x)=6e^x , [-3,3]	$f (x) = 6 e^{x}$ , $[- 3, 3]$
51227	Find the Average Rate of Change	f(x) = square root of 2x-7 from x_1=4 to x_2=6	$f (x) = \sqrt{2 x - 7}$ from $x_{1} = 4$ to $x_{2} = 6$
51228	Find the Average Rate of Change	table[[x,0],[1,2],[3,4],[y,-6],[-10,-14],[-18,-22]]	$\begin{array}{c} x & 0 \\ 1 & 2 \\ 3 & 4 \\ y & - 6 \\ - 10 & - 14 \\ - 18 & - 22 \end{array}$
51229	Find the Average Rate of Change	f(x)=10 cube root of x-5	$f (x) = 10 \sqrt[3]{x} - 5$
51230	Find the Average Rate of Change	table[[x,4],[5,6],[7,8],[9,10],[11,12],[13,14],[f(x),70],[94,102],[123,141],[162,195],[199,232],[238,251]]	$\begin{array}{c} x & 4 \\ 5 & 6 \\ 7 & 8 \\ 9 & 10 \\ 11 & 12 \\ 13 & 14 \\ f (x) & 70 \\ 94 & 102 \\ 123 & 141 \\ 162 & 195 \\ 199 & 232 \\ 238 & 251 \end{array}$
51231	Find the Average Rate of Change	x^2+2x-3 ; [-2,0]	$x^{2} + 2 x - 3$ ; $[- 2, 0]$
51232	Find the Average Rate of Change	table[[x,0],[1,2],[3,4],[g(x),1],[3,9],[27,81]]	$\begin{array}{c} x & 0 \\ 1 & 2 \\ 3 & 4 \\ g (x) & 1 \\ 3 & 9 \\ 27 & 81 \end{array}$
51233	Find the Average Rate of Change	h(t)=-16t^2+64t on [2,4]	$h (t) = - 16 t^{2} + 64 t$ on $[2, 4]$
51234	Find the Average Rate of Change	y=e^(-0.25t)	$y = e^{- 0.25 t}$
51235	Find the Average Rate of Change	f(x)=1/2x	$f (x) = \frac{1}{2} x$
51236	Find the Average Rate of Change	f(x)=(x-3)/x	$f (x) = \frac{x - 3}{x}$
51237	Find the Average Rate of Change	y=1200(0.86)^(4x)	$y = 1200 {(0.86)}^{4 x}$
51238	Find the Average Rate of Change	f(x) = cube root of x ; 4<=x<=12	$f (x) = \sqrt[3]{x}$ ; $4 \leq x \leq 12$
51239	Find the Average Rate of Change	f(x)=-1/(x^2-36)	$f (x) = \frac{- 1}{x^{2} - 36}$
51240	Find the Average Rate of Change	f(x)=2(x-2)^2+1 over the interval [-2,4]	$f (x) = 2 {(x - 2)}^{2} + 1$ over the interval $[- 2, 4]$
51241	Find the Average Rate of Change	f(x) = square root of x+1 on [0,3]	$f (x) = \sqrt{x + 1}$ on $[0, 3]$
51242	Find the Average Rate of Change	table[[x,y],[-1,1/2],[0,2],[1,8],[2,32]]	$\begin{array}{c} x & y \\ - 1 & \frac{1}{2} \\ 0 & 2 \\ 1 & 8 \\ 2 & 32 \end{array}$
51243	Find the Average Rate of Change	f(x) = square root of x+5 ; [-1,7]	$f (x) = \sqrt{x + 5}$ ; $[- 1, 7]$
51244	Find the Average Rate of Change	V(r)=4/3pir^3	$V (r) = \frac{4}{3} π r^{3}$
51245	Find the Average Rate of Change	table[[x,y],[-3,6],[-2,5 1/3],[-1,4 2/3],[0,4],[3,2]]	$\begin{array}{c} x & y \\ - 3 & 6 \\ - 2 & 5 \frac{1}{3} \\ - 1 & 4 \frac{2}{3} \\ 0 & 4 \\ 3 & 2 \end{array}$
51246	Find the Average Rate of Change	A=1200(1+i)^3	$A = 1200 {(1 + i)}^{3}$
51247	Find the Average Rate of Change	f(x) = square root of 2x-5 from x_1=3 to x_2=5	$f (x) = \sqrt{2 x - 5}$ from $x_{1} = 3$ to $x_{2} = 5$
51248	Find the Average Rate of Change	f(x)=(x-3)/x ; [5,12]	$f (x) = \frac{x - 3}{x}$ ; $[5, 12]$
51249	Find the Average Rate of Change	table[[x,y],[1,3/2],[2,9/8],[3,27/32],[4,81/128]]	$\begin{array}{c} x & y \\ 1 & \frac{3}{2} \\ 2 & \frac{9}{8} \\ 3 & \frac{27}{32} \\ 4 & \frac{81}{128} \end{array}$
51250	Find the Average Rate of Change	f(x)=(x+5)/(x-4) ; [-6,2]	$f (x) = \frac{x + 5}{x - 4}$ ; $[- 6, 2]$
51251	Find the Average Rate of Change	y=\|x\|+2	$y = \| x \| + 2$
51252	Find the Average Rate of Change	f(x)=x^3-3x^2	$f (x) = x^{3} - 3 x^{2}$
51253	Find the Average Rate of Change	w(t)=8.89+2.01t-0.0085t^2+0.000131t^3	$w (t) = 8.89 + 2.01 t - 0.0085 t^{2} + 0.000131 t^{3}$
51254	Find the Average Rate of Change	f(x)=3x^2+3 on [3,5]	$f (x) = 3 x^{2} + 3$ on $[3, 5]$
51255	Find the Average Rate of Change	f(x) = square root of 2x-1 ; [5,25]	$f (x) = \sqrt{2 x - 1}$ ; $[5, 25]$
51256	Find the Average Rate of Change	table[[x,y],[3,-5],[-2,5]]	$\begin{array}{c} x & y \\ 3 & - 5 \\ - 2 & 5 \end{array}$
51257	Find the Average Rate of Change	f(x)=-x^2+9/x , [1,6]	$f (x) = - x^{2} + \frac{9}{x}$ , $[1, 6]$
51258	Find the Average Rate of Change	table[[x,y],[1,1],[2,2],[3,3]]	$\begin{array}{c} x & y \\ 1 & 1 \\ 2 & 2 \\ 3 & 3 \end{array}$
51259	Find the Average Rate of Change	Let f(x)=- log of 4x+5	Let $f (x) = - \log (4 x) + 5$
51260	Find the Average Rate of Change	(2,-5) and (-10,3)	$(2, - 5)$ and $(- 10, 3)$
51261	Find the Average Rate of Change	f(x)=4x^2+3x on the interval [1,5] ?	$f (x) = 4 x^{2} + 3 x$ on the interval $[1, 5]$ ?
51262	Find the Average Rate of Change	f(x)=(x-1)/(x+3)	$f (x) = \frac{x - 1}{x + 3}$
51263	Find the Average Rate of Change	f(x)	$f (x)$
51264	Find the Average Rate of Change	g(t)=t^4-t^3+t^2	$g (t) = t^{4} - t^{3} + t^{2}$
51265	Find the Average Rate of Change	K_c=4 square root of 4v+1	$K_{c} = 4 \sqrt{4 v + 1}$
51266	Find the Average Rate of Change	f(x)=3x^2-x-2 on 4 , 7	$f (x) = 3 x^{2} - x - 2$ on $4$ , $7$
51267	Find the Average Rate of Change	g(x)=(x+2)/(x+3) , [0,1]	$g (x) = \frac{x + 2}{x + 3}$ , $[0, 1]$
51268	Find the Average Rate of Change	d(t)=0.8t^2	$d (t) = 0.8 t^{2}$
51269	Find the Average Rate of Change	s(t)=22/(t+1) , [0,1]	$s (t) = \frac{22}{t + 1}$ , $[0, 1]$
51270	Find the Average Rate of Change	x+4y=20	$x + 4 y = 20$
51271	Find the Average Rate of Change	f(x)=-x^2-x+1 ;, [2,7/3]	$f (x) = - x^{2} - x + 1$ ;, $[2, \frac{7}{3}]$
51272	Find the Average Rate of Change	f(x)=x^2-x-1 ; [3,13/4]	$f (x) = x^{2} - x - 1$ ; $[3, \frac{13}{4}]$
51273	Find the Average Rate of Change	f(x)=x^2-1/x-3 for 1<=x<=3	$f (x) = x^{2} - \frac{1}{x} - 3$ for $1 \leq x \leq 3$
51274	Find the Average Rate of Change	f(x) = square root of 3x-11 from x_1=4 to x_2=6	$f (x) = \sqrt{3 x - 11}$ from $x_{1} = 4$ to $x_{2} = 6$
51275	Find the Average Rate of Change	f(x) = square root of x^2-1	$f (x) = \sqrt{x^{2} - 1}$
51276	Find the Average Rate of Change	f(x) = square root of 3x-14 from x_1=5 to x_2=8	$f (x) = \sqrt{3 x - 14}$ from $x_{1} = 5$ to $x_{2} = 8$
51277	Find the Average Rate of Change	f(x)=x^3-3x^2+5	$f (x) = x^{3} - 3 x^{2} + 5$
51278	Find the Average Rate of Change	table[[x,Y],[-3,96],[-2,48],[-1,24],[0,12],[1,6],[2,3],[3,1.5]]	$\begin{array}{c} x & Y \\ - 3 & 96 \\ - 2 & 48 \\ - 1 & 24 \\ 0 & 12 \\ 1 & 6 \\ 2 & 3 \\ 3 & 1.5 \end{array}$
51279	Find the Average Rate of Change	y=1700e^(-0.074x)	$y = 1700 e^{- 0.074 x}$
51280	Find the Average Rate of Change	f(x)=x^3+x	$f (x) = x^{3} + x$
51281	Find the Average Rate of Change	table[[x,y],[-3,4],[-1,12],[1/2,-24],[2/3,-18]]	$\begin{array}{c} x & y \\ - 3 & 4 \\ - 1 & 12 \\ \frac{1}{2} & - 24 \\ \frac{2}{3} & - 18 \end{array}$
51282	Find the Average Rate of Change	table[[x,0],[1,2],[3,4],[y,40],[10,5/2],[5/8,5/32]]	$\begin{array}{c} x & 0 \\ 1 & 2 \\ 3 & 4 \\ y & 40 \\ 10 & \frac{5}{2} \\ \frac{5}{8} & \frac{5}{32} \end{array}$
51283	Find the Average Rate of Change	s(t)=120t-16t^2 , 0<=t<=7.5	$s (t) = 120 t - 16 t^{2}$ , $0 \leq t \leq 7.5$
51284	Find the Average Rate of Change	f(x) = square root of x+3 ; 2<=x<=8	$f (x) = \sqrt{x + 3}$ ; $2 \leq x \leq 8$
51285	Find the Average Rate of Change	y=a(2)^(t/3)	$y = a {(2)}^{\frac{t}{3}}$
51286	Find the Average Rate of Change	y=3sin(6theta)	$y = 3 \sin (6 θ)$
51287	Find the Average Rate of Change	f(x)=x^3-3x+3 , (-2,2)	$f (x) = x^{3} - 3 x + 3$ , $(- 2, 2)$
51288	Find the Average Rate of Change	y-2/7x=5	$y - \frac{2}{7} x = 5$
51289	Find the Average Rate of Change	y=10(1+0.4)^5	$y = 10 {(1 + 0.4)}^{5}$
51290	Find the Average Rate of Change	f(x) = square root of 2x , (2,8)	$f (x) = \sqrt{2 x}$ , $(2, 8)$
51291	Find the Average Rate of Change	f(x)=3x^2-3x+1 ; interval -5 , 5	$f (x) = 3 x^{2} - 3 x + 1$ ; interval $- 5$ , $5$
51292	Find the Average Rate of Change	d(t)=(100t)/(2t+15)	$d (t) = \frac{100 t}{2 t + 15}$
51293	Find the Average Rate of Change	f(x)=3x^3-2x^2+6 ; [2,6]	$f (x) = 3 x^{3} - 2 x^{2} + 6$ ; $[2, 6]$
51294	Find the Average Rate of Change	f(x)=1/x-x^2-2 for 3<=x<=6	$f (x) = \frac{1}{x} - x^{2} - 2$ for $3 \leq x \leq 6$
51295	Find the Average Rate of Change	f(x)=4x^2+3x on the interval [1,5]	$f (x) = 4 x^{2} + 3 x$ on the interval $[1, 5]$
51296	Find the Average Rate of Change	f(x) = square root of x+6 on [4,9]	$f (x) = \sqrt{x + 6}$ on $[4, 9]$
51297	Find the Average Rate of Change	N(p)=100-4p^2 ; 2<=p<=5	$N (p) = 100 - 4 p^{2}$ ; $2 \leq p \leq 5$
51298	Find the Average Rate of Change	P(theta)=theta^3-4theta^2+5theta ; [1,2]	$P (θ) = θ^{3} - 4 θ^{2} + 5 θ$ ; $[1, 2]$
51299	Find the Average Rate of Change	f(x)=3-x^2 -2<=x<=3	$f (x) = 3 - x^{2}$ $- 2 \leq x \leq 3$
51300	Find the Average Rate of Change	f(x)=1/(x-1) ; [-4,-11/3]	$f (x) = \frac{1}{x - 1}$ ; $[- 4, - \frac{11}{3}]$