Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
51301	Find the Average Rate of Change	y=(x+2)^2	$y = {(x + 2)}^{2}$
51302	Find the Average Rate of Change	f(x)=( square root of x^2-1)/x , 1<=x<=3	$f (x) = \frac{\sqrt{x^{2} - 1}}{x}$ , $1 \leq x \leq 3$
51303	Find the Average Rate of Change	f(x)=4x^3-4x-4 ; between 1 and 7	$f (x) = 4 x^{3} - 4 x - 4$ ; between $1$ and $7$
51304	Find the Average Rate of Change	h(t)=(t+3)*2+5	$h (t) = (t + 3) \cdot 2 + 5$
51305	Find the Average Rate of Change	f(x)=1/x on [1,3]	$f (x) = \frac{1}{x}$ on $[1, 3]$
51306	Find the Average Rate of Change	f(x) = square root of 6x	$f (x) = \sqrt{6 x}$
51307	Find the Average Rate of Change	B(t)=8500*(8/27)^(t/3)	$B (t) = 8500 \cdot {(\frac{8}{27})}^{\frac{t}{3}}$
51308	Find the Average Rate of Change	f(x)=4(2)^x+3	$f (x) = 4 {(2)}^{x} + 3$
51309	Find the Average Rate of Change	f(x)=3x^2 over the interval 1<=x<=5	$f (x) = 3 x^{2}$ over the interval $1 \leq x \leq 5$
51310	Find the Average Rate of Change	f(x)=(x+8)/(x-3)	$f (x) = \frac{x + 8}{x - 3}$
51311	Find the Average Rate of Change	f(x)=3/(x^3)	$f (x) = \frac{3}{x^{3}}$
51312	Find the Average Rate of Change	f(x)=-x^3-3x^2+4x+12[-5,1]	$f (x) = - x^{3} - 3 x^{2} + 4 x + 12 [- 5, 1]$
51313	Find the Average Rate of Change	f(t)=t^-3 ;, (1/2,8)	$f (t) = t^{- 3}$ ;, $(\frac{1}{2}, 8)$
51314	Find the Average Rate of Change	f(x)=2x^2-x-12 ; interval -3 , 3	$f (x) = 2 x^{2} - x - 12$ ; interval $- 3$ , $3$
51315	Find the Average Rate of Change	g(x)=5-x^2 on 2 , 4	$g (x) = 5 - x^{2}$ on $2$ , $4$
51316	Find the Average Rate of Change	f(x)=x^2+5x+6 on 2 , 2.1	$f (x) = x^{2} + 5 x + 6$ on $2$ , $2.1$
51317	Find the Average Rate of Change	x^2 square root of x^3+1 , [0,2]	$x^{2} \sqrt{x^{3} + 1}$ , $[0, 2]$
51318	Find the Average Rate of Change	table[[n,t(n)],[1,1],[5,-7],[10,-17]]	$\begin{array}{c} n & t (n) \\ 1 & 1 \\ 5 & - 7 \\ 10 & - 17 \end{array}$
51319	Find the Average Rate of Change	f(x)=-x(x+2)(x-3)	$f (x) = - x (x + 2) (x - 3)$
51320	Find the Average Rate of Change	f(x)=4e^x , [-2,2]	$f (x) = 4 e^{x}$ , $[- 2, 2]$
51321	Find the Average Rate of Change	f(x)=x^4-2x^3	$f (x) = x^{4} - 2 x^{3}$
51322	Find the Average Rate of Change	a_n=1/3(3)^(n-1)	$a_{n} = \frac{1}{3} {(3)}^{n - 1}$
51323	Find the Average Rate of Change	f(x)=(x^2+3)/(x-2) ; [4,9]	$f (x) = \frac{x^{2} + 3}{x - 2}$ ; $[4, 9]$
51324	Find the Average Rate of Change	g(x)=8cos(x) , [-pi/2,pi/2]	$g (x) = 8 \cos (x)$ , $[- \frac{π}{2}, \frac{π}{2}]$
51325	Find the Average Rate of Change	cos(x)	$\cos (x)$
51326	Find the Average Rate of Change	x^2+3x ; [-5,-1]	$x^{2} + 3 x$ ; $[- 5, - 1]$
51327	Find the Average Rate of Change	f(x)=cos(x) , [0,pi/2]	$f (x) = \cos (x)$ , $[0, \frac{π}{2}]$
51328	Find the Average Rate of Change	f(x) = square root of x , (16,25)	$f (x) = \sqrt{x}$ , $(16, 25)$
51329	Find the Average Rate of Change	table[[x,y],[-3,6],[-2,0],[-1,-4],[0,-6],[1,-6],[2,-4],[3,0],[4,6]]	$\begin{array}{c} x & y \\ - 3 & 6 \\ - 2 & 0 \\ - 1 & - 4 \\ 0 & - 6 \\ 1 & - 6 \\ 2 & - 4 \\ 3 & 0 \\ 4 & 6 \end{array}$
51330	Find the Average Rate of Change	f(x) = square root of x-x+1	$f (x) = \sqrt{x} - x + 1$
51331	Find the Average Rate of Change	g(x)=4x^3-2 on -3 , 3	$g (x) = 4 x^{3} - 2$ on $- 3$ , $3$
51332	Find the Average Rate of Change	f(x) = square root of x+6 on 4 , 9	$f (x) = \sqrt{x + 6}$ on $4$ , $9$
51333	Find the Average Rate of Change	f(x) = cube root of x ; [8,27]	$f (x) = \sqrt[3]{x}$ ; $[8, 27]$
51334	Find the Average Rate of Change	f(x) = square root of x+1 , (0,3)	$f (x) = \sqrt{x + 1}$ , $(0, 3)$
51335	Find the Average Rate of Change	f(x)=5-2x^2 on [-2,4]	$f (x) = 5 - 2 x^{2}$ on $[- 2, 4]$
51336	Find the Average Rate of Change	f(x)=5x^3-5x-1 ; between 1 and 6	$f (x) = 5 x^{3} - 5 x - 1$ ; between $1$ and $6$
51337	Find the Average Rate of Change	f(x)=x^3-x-1 ; between 1 and 2	$f (x) = x^{3} - x - 1$ ; between $1$ and $2$
51338	Find the Average Rate of Change	Let h(x)=x^2-4x	Let $h (x) = x^{2} - 4 x$
51339	Find the Average Rate of Change	table[[x,g(x)],[-2,2],[-1,-3],[0,2],[1,17]]	$\begin{array}{c} x & g (x) \\ - 2 & 2 \\ - 1 & - 3 \\ 0 & 2 \\ 1 & 17 \end{array}$
51340	Find the Average Rate of Change	f(x)=(x-3)^2	$f (x) = {(x - 3)}^{2}$
51341	Find the Average Rate of Change	f(x)=cos(x) , [pi,3pi]	$f (x) = \cos (x)$ , $[π, 3 π]$
51342	Find the Average Rate of Change	2t^2-t	$2 t^{2} - t$
51343	Find the Average Rate of Change	f(x)=cot(x) , [pi/6,pi/2]	$f (x) = \cot (x)$ , $[\frac{π}{6}, \frac{π}{2}]$
51344	Find the Average Rate of Change	f(x) = square root of x+1 , [0,3]	$f (x) = \sqrt{x + 1}$ , $[0, 3]$
51345	Find the Average Rate of Change	f(x)=2x^(-14/5)	$f (x) = 2 x^{- \frac{14}{5}}$
51346	Find the Average Rate of Change	f(x)=-1/8(x+1)^2+8	$f (x) = - \frac{1}{8} {(x + 1)}^{2} + 8$
51347	Find the Average Rate of Change	N(p)=100-3p^2 ; 2<=p<=5	$N (p) = 100 - 3 p^{2}$ ; $2 \leq p \leq 5$
51348	Find the Average Rate of Change	f(x)=10^(2x-2) at [1,3]	$f (x) = 10^{2 x - 2}$ at $[1, 3]$
51349	Find the Average Rate of Change	g(x)=5/(x-1)+2	$g (x) = \frac{5}{x - 1} + 2$
51350	Find the Average Rate of Change	f(x)=4x^3-3x-4 ; between 1 and 6	$f (x) = 4 x^{3} - 3 x - 4$ ; between $1$ and $6$
51351	Find the Average Rate of Change	2x^2-2 from 2 to 4	$2 x^{2} - 2$ from $2$ to $4$
51352	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 $[- 3, 1]$
51353	Find the Average Rate of Change	g(x)=(x^2)/4+7	$g (x) = \frac{x^{2}}{4} + 7$
51354	Find the Average Rate of Change	f(x)=3x natural log of x ; [1,e^2]	$f (x) = 3 x \ln (x)$ ; $[1, e^{2}]$
51355	Find the Average Rate of Change	f(x)=-5(3)^x	$f (x) = - 5 {(3)}^{x}$
51356	Find the Average Rate of Change	f(x) = square root of 3x-2 from x_1=1 to x_2=3	$f (x) = \sqrt{3 x - 2}$ from $x_{1} = 1$ to $x_{2} = 3$
51357	Find the Average Rate of Change	C(n)=22+0.1n	$C (n) = 22 + 0.1 n$
51358	Find the Average Rate of Change	f(x) = square root of 3x-8 from x_1=3 to x_2=6	$f (x) = \sqrt{3 x - 8}$ from $x_{1} = 3$ to $x_{2} = 6$
51359	Find the Average Rate of Change	y=1800e^(0.06x)	$y = 1800 e^{0.06 x}$
51360	Find the Average Rate of Change	f(x)=(x-6)/(x+4) on [1,7]	$f (x) = \frac{x - 6}{x + 4}$ on $[1, 7]$
51361	Find the Average Rate of Change	f(t)=t^3-12t^2+45t ; 0<=t<=7	$f (t) = t^{3} - 12 t^{2} + 45 t$ ; $0 \leq t \leq 7$
51362	Find the Average Rate of Change	f(x) = square root of 3x+1 , [5,8]	$f (x) = \sqrt{3 x + 1}$ , $[5, 8]$
51363	Find the Average Rate of Change	f(x)=x^2+1 on the interval [2,4]	$f (x) = x^{2} + 1$ on the interval $[2, 4]$
51364	Find the Average Rate of Change	d(t) = cube root of 6t^2	$d (t) = \sqrt[3]{6 t^{2}}$
51365	Find the Average Rate of Change	(-2,2) to (1,-4)	$(- 2, 2)$ to $(1, - 4)$
51366	Find the Average Rate of Change	(f(x+h)-f(x))/h	$\frac{f (x + h) - f (x)}{h}$
51367	Find the Average Rate of Change	f(x)=(x-2)^2+3 , [-2,1]	$f (x) = {(x - 2)}^{2} + 3$ , $[- 2, 1]$
51368	Find the Average Rate of Change	table[[x,y],[1,6],[2,4],[3,8/3],[4,16/9]]	$\begin{array}{c} x & y \\ 1 & 6 \\ 2 & 4 \\ 3 & \frac{8}{3} \\ 4 & \frac{16}{9} \end{array}$
51369	Find the Average Rate of Change	2x^3	$2 x^{3}$
51370	Find the Average Rate of Change	y=5.45+1.05(x+7)	$y = 5.45 + 1.05 (x + 7)$
51371	Find the Average Rate of Change	f(x) = square root of x+7 ; 2<=x<=10	$f (x) = \sqrt{x + 7}$ ; $2 \leq x \leq 10$
51372	Find the Average Rate of Change	r(a)=9a	$r (a) = 9 a$
51373	Find the Average Rate of Change	g(x)=4x^3-9 on [-3,3]	$g (x) = 4 x^{3} - 9$ on $[- 3, 3]$
51374	Find the Average Rate of Change	h(x)=3-5x^2 on [-2,4]	$h (x) = 3 - 5 x^{2}$ on $[- 2, 4]$
51375	Find the Average Rate of Change	f(x)=(x-4)/x ; [2,8]	$f (x) = \frac{x - 4}{x}$ ; $[2, 8]$
51376	Find the Average Rate of Change	C(n)=24+0.1n	$C (n) = 24 + 0.1 n$
51377	Find the Average Rate of Change	h(t)=(t+3)^2+5 -5<=t<=-1	$h (t) = {(t + 3)}^{2} + 5$ $- 5 \leq t \leq - 1$
51378	Find the Average Rate of Change	square root of 2x	$\sqrt{2 x}$
51379	Find the Average Rate of Change	What is the average rate of change of g(x)=2/(x+3) over the interval 1<=x<=3 ?	What is the average rate of change of $g (x) = \frac{2}{x + 3}$ over the interval $1 \leq x \leq 3$ ?
51380	Find the Average Rate of Change	f(x) = cube root of x	$f (x) = \sqrt[3]{x}$
51381	Find the Average Rate of Change	square root of 4x+1	$\sqrt{4 x + 1}$
51382	Find the Average Rate of Change	f(x)=1/x on 1 , 3	$f (x) = \frac{1}{x}$ on $1$ , $3$
51383	Find the Average Rate of Change	C=5/9(F-32)	$C = \frac{5}{9} (F - 32)$
51384	Find the Average Rate of Change	y-1/4x=1	$y - \frac{1}{4} x = 1$
51385	Find the Average Rate of Change	table[[x,y],[-2,1/4],[-1,1/2],[0,1]]	$\begin{array}{c} x & y \\ - 2 & \frac{1}{4} \\ - 1 & \frac{1}{2} \\ 0 & 1 \end{array}$
51386	Find the Average Rate of Change	table[[x,y],[-2,1/9],[-1,1/3],[0,1]]	$\begin{array}{c} x & y \\ - 2 & \frac{1}{9} \\ - 1 & \frac{1}{3} \\ 0 & 1 \end{array}$
51387	Find the Average Rate of Change	f(x)=2x+3 on [-1,2]	$f (x) = 2 x + 3$ on $[- 1, 2]$
51388	Find the Average Rate of Change	f(x)=x^3-5x-2 ; between 2 and 3	$f (x) = x^{3} - 5 x - 2$ ; between $2$ and $3$
51389	Find the Average Rate of Change	-1/2	$- \frac{1}{2}$
51390	Find the Average Rate of Change	table[[x,-4],[-2,0],[2,3],[4,6],[h(x),41],[17,1],[-7,-8],[-7,1]]	$\begin{array}{c} x & - 4 \\ - 2 & 0 \\ 2 & 3 \\ 4 & 6 \\ h (x) & 41 \\ 17 & 1 \\ - 7 & - 8 \\ - 7 & 1 \end{array}$
51391	Find the Average Rate of Change	f(x)=0.05x^2-1.3x+22.8 on 13 , 23	$f (x) = 0.05 x^{2} - 1.3 x + 22.8$ on $13$ , $23$
51392	Find the Average Rate of Change	table[[x,y],[3,5],[10,p],[15,1]]	$\begin{array}{c} x & y \\ 3 & 5 \\ 10 & p \\ 15 & 1 \end{array}$
51393	Find the Average Rate of Change	f(x)=e^(x-1)+3 , [1,5]	$f (x) = e^{x - 1} + 3$ , $[1, 5]$
51394	Find the Average Rate of Change	g(t)=-(t-1)*2+5	$g (t) = - (t - 1) \cdot 2 + 5$
51395	Find the Average Rate of Change	y=2 square root of x	$y = 2 \sqrt{x}$
51396	Find the Average Rate of Change	2 square root of x	$2 \sqrt{x}$
51397	Find the Average Rate of Change	f(x)=-(3x)/2+4	$f (x) = - \frac{3 x}{2} + 4$
51398	Find the Average Rate of Change	y=1/2x^2	$y = \frac{1}{2} x^{2}$
51399	Find the Average Rate of Change	f(x)=x^2-7 on 0 , 9	$f (x) = x^{2} - 7$ on $0$ , $9$
51400	Find the Average Rate of Change	y=-1/5x	$y = - \frac{1}{5} x$