Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
51401	Find the Average Rate of Change	g(x)=2x^3-3 on -3 , 3	$g (x) = 2 x^{3} - 3$ on $- 3$ , $3$
51402	Find the Average Rate of Change	f(x)=3 square root of x	$f (x) = 3 \sqrt{x}$
51403	Find the Average Rate of Change	(1,3) and (4,17)	$(1, 3)$ and $(4, 17)$
51404	Find the Average Rate of Change	f(x)=-2x+x^2 -2<=x<=10	$f (x) = - 2 x + x^{2}$ $- 2 \leq x \leq 10$
51405	Find the Average Rate of Change	f(x) = square root of x^3-4 over the interval 2<=x<=5	$f (x) = \sqrt{x^{3} - 4}$ over the interval $2 \leq x \leq 5$
51406	Find the Average Rate of Change	-4x^2+3x	$- 4 x^{2} + 3 x$
51407	Find the Average Rate of Change	f(x) = cube root of x ; 3<=x<=12	$f (x) = \sqrt[3]{x}$ ; $3 \leq x \leq 12$
51408	Find the Average Rate of Change	f(x)=6(2)^(2x)	$f (x) = 6 {(2)}^{2 x}$
51409	Find the Average Rate of Change	y=(0.9)t/12	$y = (0.9) \frac{t}{12}$
51410	Find the Average Rate of Change	g(t)=t/( square root of 9+t^2) , [4,9]	$g (t) = \frac{t}{\sqrt{9 + t^{2}}}$ , $[4, 9]$
51411	Find the Average Rate of Change	c(x)=2^x-1	$c (x) = 2^{x} - 1$
51412	Find the Average Rate of Change	f(x)=4 square root of x , [4,9]	$f (x) = 4 \sqrt{x}$ , $[4, 9]$
51413	Find the Average Rate of Change	h(t)=(t+3)^2+5 -4<=t<=-3	$h (t) = {(t + 3)}^{2} + 5$ $- 4 \leq t \leq - 3$
51414	Find the Average Rate of Change	F(x)=x+4	$F (x) = x + 4$
51415	Find the Average Rate of Change	table[[x,f(x)],[-4,-8],[-2,5],[-1,3],[0,0],[1,-3],[2,-5],[4,8]]	$\begin{array}{c} x & f (x) \\ - 4 & - 8 \\ - 2 & 5 \\ - 1 & 3 \\ 0 & 0 \\ 1 & - 3 \\ 2 & - 5 \\ 4 & 8 \end{array}$
51416	Find the Average Rate of Change	h(x)=5-4x^2 on -2 , 4	$h (x) = 5 - 4 x^{2}$ on $- 2$ , $4$
51417	Find the Average Rate of Change	k(x)=10^x , given -3<=x<=1	$k (x) = 10^{x}$ , given $- 3 \leq x \leq 1$
51418	Find the Average Rate of Change	f(x)=4x^3 ; [1,3]	$f (x) = 4 x^{3}$ ; $[1, 3]$
51419	Find the Average Rate of Change	f(x)=\|2x+3\|	$f (x) = \| 2 x + 3 \|$
51420	Find the Average Rate of Change	f(x)=2x^2+3x-3 ; intervals [-2,2]	$f (x) = 2 x^{2} + 3 x - 3$ ; intervals $[- 2, 2]$
51421	Find the Average Rate of Change	f(x) = square root of x+9 on [-4,2]	$f (x) = \sqrt{x + 9}$ on $[- 4, 2]$
51422	Find the Average Rate of Change	h(x)=-2x^2-3x-1 on the interval [1,5]	$h (x) = - 2 x^{2} - 3 x - 1$ on the interval $[1, 5]$
51423	Find the Average Rate of Change	f(x)=-sin(x) , [0,pi]	$f (x) = - \sin (x)$ , $[0, π]$
51424	Find the Average Rate of Change	f(x) = square root of 2x+8 on the interval [-2,5]	$f (x) = \sqrt{2 x + 8}$ on the interval $[- 2, 5]$
51425	Find the Average Rate of Change	table[[x,y],[-2,1/9],[-1,1/3],[0,1],[1,3],[2,9]]	$\begin{array}{c} x & y \\ - 2 & \frac{1}{9} \\ - 1 & \frac{1}{3} \\ 0 & 1 \\ 1 & 3 \\ 2 & 9 \end{array}$
51426	Find the Average Rate of Change	f(x)=3x^2-x^3[1,5]	$f (x) = 3 x^{2} - x^{3} [1, 5]$
51427	Find the Average Rate of Change	g(x)=2x^3-5 on [-3,3]	$g (x) = 2 x^{3} - 5$ on $[- 3, 3]$
51428	Find the Average Rate of Change	p(t)=((t^2-4)(t+1))/(t^2+3) on [-3,1]	$p (t) = \frac{(t^{2} - 4) (t + 1)}{t^{2} + 3}$ on $[- 3, 1]$
51429	Find the Average Rate of Change	f(x)=2x^3-2x-4 ; between 1 and 5	$f (x) = 2 x^{3} - 2 x - 4$ ; between $1$ and $5$
51430	Find the Average Rate of Change	4y+x=1	$4 y + x = 1$
51431	Find the Average Rate of Change	N(t)=-0.023(t-33.12)^2+131 , 0<=t<=14	$N (t) = - 0.023 {(t - 33.12)}^{2} + 131$ , $0 \leq t \leq 14$
51432	Find the Average Rate of Change	-2x^3+4x^2	$- 2 x^{3} + 4 x^{2}$
51433	Find the Average Rate of Change	f(x)=x^2+3x over [-1,1]	$f (x) = x^{2} + 3 x$ over $[- 1, 1]$
51434	Find the Average Rate of Change	f(x)=- log of 4x+5	$f (x) = - \log (4 x) + 5$
51435	Find the Average Rate of Change	table[[x,f(x)],[216,3],[1296,4],[7776,5]]	$\begin{array}{c} x & f (x) \\ 216 & 3 \\ 1296 & 4 \\ 7776 & 5 \end{array}$
51436	Find the Average Rate of Change	f(x)=1/(2x)-5 -1<=x<=1	$f (x) = \frac{1}{2 x} - 5$ $- 1 \leq x \leq 1$
51437	Find the Average Rate of Change	a_n=12+(n-1)(-8)	$a_{n} = 12 + (n - 1) (- 8)$
51438	Find the Average Rate of Change	(-2,8) to (1,-4)	$(- 2, 8)$ to $(1, - 4)$
51439	Find the Average Rate of Change	f(x)=cos(x) , [-pi/3,pi/3]	$f (x) = \cos (x)$ , $[- \frac{π}{3}, \frac{π}{3}]$
51440	Find the Average Rate of Change	f(x)=arctan(x^2) on -2 , 2	$f (x) = \arctan (x^{2})$ on $- 2$ , $2$
51441	Find the Average Rate of Change	f(x)=x+x^4	$f (x) = x + x^{4}$
51442	Find the Average Rate of Change	h(x)=x^3+2x^2-x-1[0,5]	$h (x) = x^{3} + 2 x^{2} - x - 1 [0, 5]$
51443	Find the Average Rate of Change	f(x)=(x-2)/(x^2-2x)	$f (x) = \frac{x - 2}{x^{2} - 2 x}$
51444	Find the Average Rate of Change	f(x)=(x-2)^2+3 , [-2,1]	$f (x) = {(x - 2)}^{2} + 3$ , $[- 2, 1]$
51445	Find the Average Rate of Change	table[[x,1],[2,3],[4,5],[f(x),-2],[3,8],[13,18]]	$\begin{array}{c} x & 1 \\ 2 & 3 \\ 4 & 5 \\ f (x) & - 2 \\ 3 & 8 \\ 13 & 18 \end{array}$
51446	Find the Average Rate of Change	table[[x,y],[1,6],[2,4],[3,8/3]]	$\begin{array}{c} x & y \\ 1 & 6 \\ 2 & 4 \\ 3 & \frac{8}{3} \end{array}$
51447	Find the Average Rate of Change	y=5x^4-4x^3+25x+8000	$y = 5 x^{4} - 4 x^{3} + 25 x + 8000$
51448	Find the Average Rate of Change	f(X)=4/3x+8	$f (X) = \frac{4}{3} x + 8$
51449	Find the Average Rate of Change	f(x)=2x , [3,5]	$f (x) = 2 x$ , $[3, 5]$
51450	Find the Average Rate of Change	f(x)=x^3-3x-4 ; between 2 and 4	$f (x) = x^{3} - 3 x - 4$ ; between $2$ and $4$
51451	Find the Average Rate of Change	f(x)=x^5-x^4+8x^3-8x^2-15x+15 ; [1.2,1.3]	$f (x) = x^{5} - x^{4} + 8 x^{3} - 8 x^{2} - 15 x + 15$ ; $[1.2, 1.3]$
51452	Find the Average Rate of Change	s(t)=4sin(t) , [pi/2,pi]	$s (t) = 4 \sin (t)$ , $[\frac{π}{2}, π]$
51453	Find the Average Rate of Change	(50,34.3) and (60,25.8)	$(50, 34.3)$ and $(60, 25.8)$
51454	Find the Average Rate of Change	f(x)=3x^2-5 on the interval -3<=x<=1	$f (x) = 3 x^{2} - 5$ on the interval $- 3 \leq x \leq 1$
51455	Find the Average Rate of Change	f(x)=(3x-6)/(x-2)	$f (x) = \frac{3 x - 6}{x - 2}$
51456	Find the Average Rate of Change	table[[x,y],[5,2],[5,4],[5,6],[5,8],[5,10]]	$\begin{array}{c} x & y \\ 5 & 2 \\ 5 & 4 \\ 5 & 6 \\ 5 & 8 \\ 5 & 10 \end{array}$
51457	Find the Average Rate of Change	y=- square root of x-4+5	$y = - \sqrt{x - 4 + 5}$
51458	Find the Average Rate of Change	f(x)=-x^2+9/x , [1,6]	$f (x) = - x^{2} + \frac{9}{x}$ , $[1, 6]$
51459	Find the Average Rate of Change	g(x)=8x^3-9 on [-3,3]	$g (x) = 8 x^{3} - 9$ on $[- 3, 3]$
51460	Find the Average Rate of Change	h(x)=1/(10-x) over the interval 5<=x<=8 ?	$h (x) = \frac{1}{10 - x}$ over the interval $5 \leq x \leq 8$ ?
51461	Find the Average Rate of Change	f(x)=20/(1+9e^(-3x))	$f (x) = \frac{20}{1 + 9 e^{- 3 x}}$
51462	Find the Average Rate of Change	f(x)=-3+x^2	$f (x) = - 3 + x^{2}$
51463	Find the Average Rate of Change	f(x)=x-4 square root of x	$f (x) = x - 4 \sqrt{x}$
51464	Find the Average Rate of Change	g(x) = cube root of x+2 ; -3<=x<=0	$g (x) = \sqrt[3]{x} + 2$ ; $- 3 \leq x \leq 0$
51465	Find the Average Rate of Change	P(theta)=theta^3-4theta^2+5theta , [1,2]	$P (θ) = θ^{3} - 4 θ^{2} + 5 θ$ , $[1, 2]$
51466	Find the Average Rate of Change	table[[x,-3],[2,5],[11,f(x)],[-130,0],[78,234]]	$\begin{array}{c} x & - 3 \\ 2 & 5 \\ 11 & f (x) \\ - 130 & 0 \\ 78 & 234 \end{array}$
51467	Find the Average Rate of Change	f(x)=5-2x^2 , (-2,4)	$f (x) = 5 - 2 x^{2}$ , $(- 2, 4)$
51468	Find the Average Rate of Change	f(x)=3x-8 interval: 4 , 5	$f (x) = 3 x - 8$ interval: $4$ , $5$
51469	Find the Average Rate of Change	f(x)=9+4x-4x^2 ; [0,5]	$f (x) = 9 + 4 x - 4 x^{2}$ ; $[0, 5]$
51470	Find the Average Rate of Change	f(x) = square root of x+5 , 0<=x<=9	$f (x) = \sqrt{x} + 5$ , $0 \leq x \leq 9$
51471	Find the Average Rate of Change	30(1.05)^3	$30 {(1.05)}^{3}$
51472	Find the Average Rate of Change	f(x)=cot(x) , [pi/6,(3pi)/2]	$f (x) = \cot (x)$ , $[\frac{π}{6}, \frac{3 π}{2}]$
51473	Find the Average Rate of Change	table[[1930,22.1],[1960,36.4],[1980,54.3],[2000,79.6],[2009,96.7]]	$\begin{array}{c} 1930 & 22.1 \\ 1960 & 36.4 \\ 1980 & 54.3 \\ 2000 & 79.6 \\ 2009 & 96.7 \end{array}$
51474	Find the Average Rate of Change	A=pir^2	$A = π r^{2}$
51475	Find the Average Rate of Change	f(x)=(x-1)^2	$f (x) = {(x - 1)}^{2}$
51476	Find the Average Rate of Change	f(x)=4x-x^2+5 2<=x<=4	$f (x) = 4 x - x^{2} + 5$ $2 \leq x \leq 4$
51477	Find the Average Rate of Change	f(x)=1/5x^5-3x^3+2 , [0,1]	$f (x) = \frac{1}{5} x^{5} - 3 x^{3} + 2$ , $[0, 1]$
51478	Find the Average Rate of Change	C(x)=1.74x^2	$C (x) = 1.74 x^{2}$
51479	Find the Average Rate of Change	h(x)=9-8x^2 on -2 , 4	$h (x) = 9 - 8 x^{2}$ on $- 2$ , $4$
51480	Find the Average Rate of Change	table[[n,a_n],[1,5],[2,10],[3,20],[4,40],[5,80]]	$\begin{array}{c} n & a_{n} \\ 1 & 5 \\ 2 & 10 \\ 3 & 20 \\ 4 & 40 \\ 5 & 80 \end{array}$
51481	Find the Average Rate of Change	f(x)=(x^2-1)/(x-1)	$f (x) = \frac{x^{2} - 1}{x - 1}$
51482	Find the Average Rate of Change	f(x)=1/2x^2+9	$f (x) = \frac{1}{2} x^{2} + 9$
51483	Find the Average Rate of Change	2x^2+x+5	$2 x^{2} + x + 5$
51484	Find the Average Rate of Change	y=128(1/2)^x	$y = 128 {(\frac{1}{2})}^{x}$
51485	Find the Average Rate of Change	-5-7/8x=y	$- 5 - \frac{7}{8} x = y$
51486	Find the Average Rate of Change	table[[x,V(x)],[0,4],[1,5.4],[2,7.29],[3,9.84]]	$\begin{array}{c} x & V (x) \\ 0 & 4 \\ 1 & 5.4 \\ 2 & 7.29 \\ 3 & 9.84 \end{array}$
51487	Find the Average Rate of Change	h(x)=6-4x^2 on -2 , 4	$h (x) = 6 - 4 x^{2}$ on $- 2$ , $4$
51488	Find the Average Rate of Change	table[[n,t(n)],[1,10],[2,18],[3,32.4]]	$\begin{array}{c} n & t (n) \\ 1 & 10 \\ 2 & 18 \\ 3 & 32.4 \end{array}$
51489	Find the Average Rate of Change	a_n=1/2(2)^(n-1)	$a_{n} = \frac{1}{2} {(2)}^{n - 1}$
51490	Find the Average Rate of Change	g(x) = cube root of x+4 ; -5<=x<=0	$g (x) = \sqrt[3]{x} + 4$ ; $- 5 \leq x \leq 0$
51491	Find the Average Rate of Change	table[[t,S],[0.5,11.25],[2,9],[5,4.5]]	$\begin{array}{c} t & S \\ 0.5 & 11.25 \\ 2 & 9 \\ 5 & 4.5 \end{array}$
51492	Find the Average Rate of Change	f(x)=(1/3)^x	$f (x) = {(\frac{1}{3})}^{x}$
51493	Find the Average Rate of Change	(-2,10) to (1,-2)	$(- 2, 10)$ to $(1, - 2)$
51494	Find the Average Rate of Change	f(x)=x^2-1/x , [2,4]	$f (x) = x^{2} - \frac{1}{x}$ , $[2, 4]$
51495	Find the Average Rate of Change	f(x)=x^(3/2) on 1 , 4	$f (x) = x^{\frac{3}{2}}$ on $1$ , $4$
51496	Find the Average Rate of Change	f(x)=1/2x^2+1/4x	$f (x) = \frac{1}{2} x^{2} + \frac{1}{4} x$
51497	Find the Average Rate of Change	s(t)=-16t^2+288t+304 for 0<=t<=19	$s (t) = - 16 t^{2} + 288 t + 304$ for $0 \leq t \leq 19$
51498	Find the Average Rate of Change	N(w)=7e^(0.2w) , [17,24]	$N (w) = 7 e^{0.2 w}$ , $[17, 24]$
51499	Find the Average Rate of Change	2x+h	$2 x + h$
51500	Find the Average Rate of Change	f(x)=- natural log of x+1	$f (x) = - \ln (x + 1)$