Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
51101	Find the Average Rate of Change	f(x) = square root of 3x-8 from x_1=3 to x_2=5	$f (x) = \sqrt{3 x - 8}$ from $x_{1} = 3$ to $x_{2} = 5$
51102	Find the Average Rate of Change	h(x)=x^2-1 -3<=x<=-1	$h (x) = x^{2} - 1$ $- 3 \leq x \leq - 1$
51103	Find the Average Rate of Change	y = log base 1/2 of x	$y = \log_{\frac{1}{2}} (x)$
51104	Find the Average Rate of Change	f(x)=cos(x)	$f (x) = \cos (x)$
51105	Find the Average Rate of Change	g(x)=x^3-x on 4 , 5	$g (x) = x^{3} - x$ on $4$ , $5$
51106	Find the Average Rate of Change	y=100-15x	$y = 100 - 15 x$
51107	Find the Average Rate of Change	M(t)=200*(0.96)^t	$M (t) = 200 \cdot {(0.96)}^{t}$
51108	Find the Average Rate of Change	f(x)=1/2(3)^x	$f (x) = \frac{1}{2} {(3)}^{x}$
51109	Find the Average Rate of Change	square root of 3x+1	$\sqrt{3 x + 1}$
51110	Find the Average Rate of Change	f(x)=3x^2-x^3 , [1,5]	$f (x) = 3 x^{2} - x^{3}$ , $[1, 5]$
51111	Find the Average Rate of Change	f(x) = square root of 2x-7 from x_1=4 to x_2=7	$f (x) = \sqrt{2 x - 7}$ from $x_{1} = 4$ to $x_{2} = 7$
51112	Find the Average Rate of Change	f(x)=x^2+x-1 ; [-2,-7/4]	$f (x) = x^{2} + x - 1$ ; $[- 2, - \frac{7}{4}]$
51113	Find the Average Rate of Change	(2,3) and (-4,-1)	$(2, 3)$ and $(- 4, - 1)$
51114	Find the Average Rate of Change	f(x) = square root of 3x-14 from x_1=5 to x_2=7	$f (x) = \sqrt{3 x - 14}$ from $x_{1} = 5$ to $x_{2} = 7$
51115	Find the Average Rate of Change	g(x)=-(x^2)/4+7 , [-2,4]	$g (x) = - \frac{x^{2}}{4} + 7$ , $[- 2, 4]$
51116	Find the Average Rate of Change	table[[x,f(x)],[2,25],[3,125],[4,625]]	$\begin{array}{c} x & f (x) \\ 2 & 25 \\ 3 & 125 \\ 4 & 625 \end{array}$
51117	Find the Average Rate of Change	table[[x,y],[-2,1/5],[-1,1],[0,5],[1,25],[2,125]]	$\begin{array}{c} x & y \\ - 2 & \frac{1}{5} \\ - 1 & 1 \\ 0 & 5 \\ 1 & 25 \\ 2 & 125 \end{array}$
51118	Find the Average Rate of Change	h(t)=-16t^2+96t on [3,6]	$h (t) = - 16 t^{2} + 96 t$ on $[3, 6]$
51119	Find the Average Rate of Change	f(x)=3^x+2 ; over the interval 1<=x<=4	$f (x) = 3^{x} + 2$ ; over the interval $1 \leq x \leq 4$
51120	Find the Average Rate of Change	f(x)=1/5x^5-3x^3+2 , [0,1]	$f (x) = \frac{1}{5} x^{5} - 3 x^{3} + 2$ , $[0, 1]$
51121	Find the Average Rate of Change	table[[n,1],[2,3],[4,a_n],[7640,764],[76.4,7.64]]	$\begin{array}{c} n & 1 \\ 2 & 3 \\ 4 & a_{n} \\ 7640 & 764 \\ 76.4 & 7.64 \end{array}$
51122	Find the Average Rate of Change	f(x)=(-x^2)/(x^3-x^2)	$f (x) = \frac{- x^{2}}{x^{3} - x^{2}}$
51123	Find the Average Rate of Change	f(x)=-x^3+2x^2-9 -1<=x<=3	$f (x) = - x^{3} + 2 x^{2} - 9$ $- 1 \leq x \leq 3$
51124	Find the Average Rate of Change	table[[x,Y],[-9,-63],[-7,-49],[-4,-28],[-3,-21],[4,28]]	$\begin{array}{c} x & Y \\ - 9 & - 63 \\ - 7 & - 49 \\ - 4 & - 28 \\ - 3 & - 21 \\ 4 & 28 \end{array}$
51125	Find the Average Rate of Change	R(x)=100x-0.03x^2	$R (x) = 100 x - 0.03 x^{2}$
51126	Find the Average Rate of Change	t(x)=x^3(8-x^2)+98.6	$t (x) = x^{3} (8 - x^{2}) + 98.6$
51127	Find the Average Rate of Change	table[[t,P(t)],[0,6.71],[3,6.26],[4,6],[9,3.41]]	$\begin{array}{c} t & P (t) \\ 0 & 6.71 \\ 3 & 6.26 \\ 4 & 6 \\ 9 & 3.41 \end{array}$
51128	Find the Average Rate of Change	b(x)=x^2+2	$b (x) = x^{2} + 2$
51129	Find the Average Rate of Change	h(w)=0.11w^1.36	$h (w) = 0.11 w^{1.36}$
51130	Find the Average Rate of Change	f(x)=18+3e^(-3x)	$f (x) = 18 + 3 e^{- 3 x}$
51131	Find the Average Rate of Change	g(x)=9x^3-8 on [-3,3]	$g (x) = 9 x^{3} - 8$ on $[- 3, 3]$
51132	Find the Average Rate of Change	3280(1.0117)^(12t)	$3280 {(1.0117)}^{12 t}$
51133	Find the Average Rate of Change	y = square root of x	$y = \sqrt{x}$
51134	Find the Average Rate of Change	y=55*(1-0.02)^t	$y = 55 \cdot {(1 - 0.02)}^{t}$
51135	Find the Average Rate of Change	f(x)=24/(1+3e^(-1.3x))	$f (x) = \frac{24}{1 + 3 e^{- 1.3 x}}$
51136	Find the Average Rate of Change	f(x)=x^3-9x[1,6]	$f (x) = x^{3} - 9 x [1, 6]$
51137	Find the Average Rate of Change	g(x)=1/2(2)^(x-1)	$g (x) = \frac{1}{2} {(2)}^{x - 1}$
51138	Find the Average Rate of Change	table[[x,q(x)],[1,2],[9,162],[2,8],[8,128],[3,18]]	$\begin{array}{c} x & q (x) \\ 1 & 2 \\ 9 & 162 \\ 2 & 8 \\ 8 & 128 \\ 3 & 18 \end{array}$
51139	Find the Average Rate of Change	f(x)=x^2-4x-12 on -1 , 7	$f (x) = x^{2} - 4 x - 12$ on $- 1$ , $7$
51140	Find the Average Rate of Change	f(x)=3/(x^2+2)	$f (x) = \frac{3}{x^{2} + 2}$
51141	Find the Average Rate of Change	f(x) = fourth root of x ; [1,16]	$f (x) = \sqrt[4]{x}$ ; $[1, 16]$
51142	Find the Average Rate of Change	y=1.2^(x+4)-2	$y = {1.2}^{(x + 4)} - 2$
51143	Find the Average Rate of Change	g(x)=4x^3-5 on -3 , 3	$g (x) = 4 x^{3} - 5$ on $- 3$ , $3$
51144	Find the Average Rate of Change	F(t)=t^2+3t-5	$F (t) = t^{2} + 3 t - 5$
51145	Find the Average Rate of Change	y=- square root of 2x+5	$y = - \sqrt{2 x + 5}$
51146	Find the Average Rate of Change	r(x)=100x-0.05x^2	$r (x) = 100 x - 0.05 x^{2}$
51147	Find the Average Rate of Change	table[[x,0],[2,4],[6,8],[y,15],[9,3],[-3,-9]]	$\begin{array}{c} x & 0 \\ 2 & 4 \\ 6 & 8 \\ y & 15 \\ 9 & 3 \\ - 3 & - 9 \end{array}$
51148	Find the Average Rate of Change	f(x)=x/(3x^2-5x)	$f (x) = \frac{x}{3 x^{2} - 5 x}$
51149	Find the Average Rate of Change	f(x)=x^3-4x^2-x+5 on 0 , 4	$f (x) = x^{3} - 4 x^{2} - x + 5$ on $0$ , $4$
51150	Find the Average Rate of Change	f(x)=cot(x) , [(3pi)/4,(5pi)/4]	$f (x) = \cot (x)$ , $[\frac{3 π}{4}, \frac{5 π}{4}]$
51151	Find the Average Rate of Change	(t+3)^2+5	${(t + 3)}^{2} + 5$
51152	Find the Average Rate of Change	f(x)=e^x	$f (x) = e^{x}$
51153	Find the Average Rate of Change	f(x) = square root of 2x-1 from x_1=1 to x_2=4	$f (x) = \sqrt{2 x - 1}$ from $x_{1} = 1$ to $x_{2} = 4$
51154	Find the Average Rate of Change	sin(x)	$\sin (x)$
51155	Find the Average Rate of Change	b(x)=36x^2 for 1<=x<=30	$b (x) = 36 x^{2}$ for $1 \leq x \leq 30$
51156	Find the Average Rate of Change	g(x)=2x^2-4x on [-1,3]	$g (x) = 2 x^{2} - 4 x$ on $[- 1, 3]$
51157	Find the Average Rate of Change	f(x)=5/(x^2+1) ; [-1,1]	$f (x) = \frac{5}{x^{2} + 1}$ ; $[- 1, 1]$
51158	Find the Average Rate of Change	f(x)=x^(3/2) on [1,4]	$f (x) = x^{\frac{3}{2}}$ on $[1, 4]$
51159	Find the Average Rate of Change	f(x)=x^2-2x-8 on -1 , 3	$f (x) = x^{2} - 2 x - 8$ on $- 1$ , $3$
51160	Find the Average Rate of Change	f(x)=0.03(10x-x^2)	$f (x) = 0.03 (10 x - x^{2})$
51161	Find the Average Rate of Change	square root of x	$\sqrt{x}$
51162	Find the Average Rate of Change	table[[x,y],[1,2],[2,2/5],[3,2/25]]	$\begin{array}{c} x & y \\ 1 & 2 \\ 2 & \frac{2}{5} \\ 3 & \frac{2}{25} \end{array}$
51163	Find the Average Rate of Change	f(x)=4/(x^2+1) ; [-1,1]	$f (x) = \frac{4}{x^{2} + 1}$ ; $[- 1, 1]$
51164	Find the Average Rate of Change	f(x)=x^2 on [2,5]	$f (x) = x^{2}$ on $[2, 5]$
51165	Find the Average Rate of Change	V=4/3pir^3	$V = \frac{4}{3} π r^{3}$
51166	Find the Average Rate of Change	f(x)=5x^2 , over the interval 2<=x<=4 ?	$f (x) = 5 x^{2}$ , over the interval $2 \leq x \leq 4$ ?
51167	Find the Average Rate of Change	f(x)=x^2+x-1 ;, [-2,-7/4]	$f (x) = x^{2} + x - 1$ ;, $[- 2, - \frac{7}{4}]$
51168	Find the Average Rate of Change	C(t)=(0.2t)/(t^2+4)	$C (t) = \frac{0.2 t}{t^{2} + 4}$
51169	Find the Average Rate of Change	table[[x,y],[1/4,-1],[1/8,1/2],[0,2]]	$\begin{array}{c} x & y \\ \frac{1}{4} & - 1 \\ \frac{1}{8} & \frac{1}{2} \\ 0 & 2 \end{array}$
51170	Find the Average Rate of Change	V=(4pir^3)/3	$V = \frac{4 π r^{3}}{3}$
51171	Find the Average Rate of Change	f(x)=5x^3-4x-4 ; between 1 and 5	$f (x) = 5 x^{3} - 4 x - 4$ ; between $1$ and $5$
51172	Find the Average Rate of Change	f(x)=-(5)^(x-3)+2	$f (x) = - {(5)}^{x - 3} + 2$
51173	Find the Average Rate of Change	table[[x,-3],[-1,1/2],[2/3,y],[4,12],[-24,-18]]	$\begin{array}{c} x & - 3 \\ - 1 & \frac{1}{2} \\ \frac{2}{3} & y \\ 4 & 12 \\ - 24 & - 18 \end{array}$
51174	Find the Average Rate of Change	f(x)=-(2)^x-1 ; over the interval 2<=x<=5	$f (x) = - {(2)}^{x} - 1$ ; over the interval $2 \leq x \leq 5$
51175	Find the Average Rate of Change	D(p)=-2p^2-3p+900	$D (p) = - 2 p^{2} - 3 p + 900$
51176	Find the Average Rate of Change	table[[x,q(x)],[6,12],[3,6],[8,16],[12,24]]	$\begin{array}{c} x & q (x) \\ 6 & 12 \\ 3 & 6 \\ 8 & 16 \\ 12 & 24 \end{array}$
51177	Find the Average Rate of Change	(-2,4) to (1,-5)	$(- 2, 4)$ to $(1, - 5)$
51178	Find the Average Rate of Change	f(x)=- cube root of x	$f (x) = - \sqrt[3]{x}$
51179	Find the Average Rate of Change	f(x)=2(x-2)^2+1 , [-2,4]	$f (x) = 2 {(x - 2)}^{2} + 1$ , $[- 2, 4]$
51180	Find the Average Rate of Change	Find the point on the curve f(x)=x^2 closest to the point (3,4)	Find the point on the curve $f (x) = x^{2}$ closest to the point $(3, 4)$
51181	Find the Average Rate of Change	f(x)=x^2-4x+2[-2,2]	$f (x) = x^{2} - 4 x + 2 [- 2, 2]$
51182	Find the Average Rate of Change	N(x)=90(0.86)^x+69	$N (x) = 90 {(0.86)}^{x} + 69$
51183	Find the Average Rate of Change	(f(b)-f(a))/(b-a)	$\frac{f (b) - f (a)}{b - a}$
51184	Find the Average Rate of Change	y=3sin(2x)	$y = 3 \sin (2 x)$
51185	Find the Average Rate of Change	f(x) = square root of 3x-11 from x_1=4 to x_2=7	$f (x) = \sqrt{3 x - 11}$ from $x_{1} = 4$ to $x_{2} = 7$
51186	Find the Average Rate of Change	h(t)=-16t^2+128t on [4,8]	$h (t) = - 16 t^{2} + 128 t$ on $[4, 8]$
51187	Find the Average Rate of Change	7/9	$\frac{7}{9}$
51188	Find the Average Rate of Change	g(x)=-(x^2)/4+7[-2,4]	$g (x) = - \frac{x^{2}}{4} + 7 [- 2, 4]$
51189	Find the Average Rate of Change	f(x) = square root of 2x-5 from x_1=3 to x_2=6	$f (x) = \sqrt{2 x - 5}$ from $x_{1} = 3$ to $x_{2} = 6$
51190	Find the Average Rate of Change	y=1/3x^2-4	$y = \frac{1}{3} x^{2} - 4$
51191	Find the Average Rate of Change	f(x)=4x^5-9x^2+8	$f (x) = 4 x^{5} - 9 x^{2} + 8$
51192	Find the Average Rate of Change	f(x)=sin(x) , [0,pi/6]	$f (x) = \sin (x)$ , $[0, \frac{π}{6}]$
51193	Find the Average Rate of Change	v(t)=3t-2 , 0<=t<=3	$v (t) = 3 t - 2$ , $0 \leq t \leq 3$
51194	Find the Average Rate of Change	f(x)=4x^3-2x-5 ; between 1 and 3	$f (x) = 4 x^{3} - 2 x - 5$ ; between $1$ and $3$
51195	Find the Average Rate of Change	f(x)=3x^2 , [1,3]	$f (x) = 3 x^{2}$ , $[1, 3]$
51196	Find the Average Rate of Change	s(t)=22/(t+1) , [0,0.5]	$s (t) = \frac{22}{t + 1}$ , $[0, 0.5]$
51197	Find the Average Rate of Change	table[[x,y],[-1,-2],[-1,-1],[-1,0],[-1,1],[-1,2],[-1,8]]	$\begin{array}{c} x & y \\ - 1 & - 2 \\ - 1 & - 1 \\ - 1 & 0 \\ - 1 & 1 \\ - 1 & 2 \\ - 1 & 8 \end{array}$
51198	Find the Average Rate of Change	table[[x,y],[1,-1],[4,8]]	$\begin{array}{c} x & y \\ 1 & - 1 \\ 4 & 8 \end{array}$
51199	Find the Average Rate of Change	f(x) = square root of x+8 ; [4,10]	$f (x) = \sqrt{x + 8}$ ; $[4, 10]$
51200	Find the Average Rate of Change	f(x)=cos(x) , [-pi/3,pi/3]	$f (x) = \cos (x)$ , $[- \frac{π}{3}, \frac{π}{3}]$