Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
51001	Find the Average Rate of Change	1/3x-4	$\frac{1}{3} x - 4$
51002	Find the Average Rate of Change	y = square root of x^3+1 at (2,3)	$y = \sqrt{x^{3} + 1}$ at $(2, 3)$
51003	Find the Average Rate of Change	3x^2	$3 x^{2}$
51004	Find the Average Rate of Change	y=1/x	$y = \frac{1}{x}$
51005	Find the Average Rate of Change	g(t)=-(t-1)^2+5 -4<=t<=5	$g (t) = - {(t - 1)}^{2} + 5$ $- 4 \leq t \leq 5$
51006	Find the Average Rate of Change	3x^2-2	$3 x^{2} - 2$
51007	Find the Average Rate of Change	f(x)=x^3-5x-5 ; between 1 and 4	$f (x) = x^{3} - 5 x - 5$ ; between $1$ and $4$
51008	Find the Average Rate of Change	3y=2x+5	$3 y = 2 x + 5$
51009	Find the Average Rate of Change	table[[x,q(x)],[0,0.0625],[1,0.25],[2,1],[3,4]]	$\begin{array}{c} x & q (x) \\ 0 & 0.0625 \\ 1 & 0.25 \\ 2 & 1 \\ 3 & 4 \end{array}$
51010	Find the Average Rate of Change	table[[x,f(x)],[-1,1/2],[0,1],[1,2],[2,4],[3,8]]	$\begin{array}{c} x & f (x) \\ - 1 & \frac{1}{2} \\ 0 & 1 \\ 1 & 2 \\ 2 & 4 \\ 3 & 8 \end{array}$
51011	Find the Average Rate of Change	P(x)=x^3-13x+12	$P (x) = x^{3} - 13 x + 12$
51012	Find the Average Rate of Change	f(x)=2x^2-4x+1 1<x<=4	$f (x) = 2 x^{2} - 4 x + 1$ $1 < x \leq 4$
51013	Find the Average Rate of Change	table[[x,f(x)],[-1,1/4],[0,1],[1,4],[2,16],[3,64]]	$\begin{array}{c} x & f (x) \\ - 1 & \frac{1}{4} \\ 0 & 1 \\ 1 & 4 \\ 2 & 16 \\ 3 & 64 \end{array}$
51014	Find the Average Rate of Change	f(x)=cot(x) , [pi/3,pi/2]	$f (x) = \cot (x)$ , $[\frac{π}{3}, \frac{π}{2}]$
51015	Find the Average Rate of Change	y=k	$y = k$
51016	Find the Average Rate of Change	table[[x,y],[0,4],[1,2],[2,1],[3,1/2],[4,1/4]]	$\begin{array}{c} x & y \\ 0 & 4 \\ 1 & 2 \\ 2 & 1 \\ 3 & \frac{1}{2} \\ 4 & \frac{1}{4} \end{array}$
51017	Find the Average Rate of Change	y=x^2+9x	$y = x^{2} + 9 x$
51018	Find the Average Rate of Change	y = square root of 2x	$y = \sqrt{2 x}$
51019	Find the Average Rate of Change	f(x)=-x^3+3x^2-2	$f (x) = - x^{3} + 3 x^{2} - 2$
51020	Find the Average Rate of Change	f(x)=-x^2+2x+2[0,3]	$f (x) = - x^{2} + 2 x + 2 [0, 3]$
51021	Find the Average Rate of Change	-1+3/4x=y	$- 1 + \frac{3}{4} x = y$
51022	Find the Average Rate of Change	f(x)=-x^3+6x^2+x	$f (x) = - x^{3} + 6 x^{2} + x$
51023	Find the Average Rate of Change	f(t)=(94t)/(99t-94)	$f (t) = \frac{94 t}{99 t - 94}$
51024	Find the Average Rate of Change	f(x) = cube root of x+3	$f (x) = \sqrt[3]{x + 3}$
51025	Find the Average Rate of Change	f(2)=3^6+25	$f (2) = 3^{6} + 25$
51026	Find the Average Rate of Change	table[[x,y],[0,1/3],[3,2],[6,12]]	$\begin{array}{c} x & y \\ 0 & \frac{1}{3} \\ 3 & 2 \\ 6 & 12 \end{array}$
51027	Find the Average Rate of Change	f(x)=4x-x^2	$f (x) = 4 x - x^{2}$
51028	Find the Average Rate of Change	f(x)=5x^4-4x^3+25x+8000	$f (x) = 5 x^{4} - 4 x^{3} + 25 x + 8000$
51029	Find the Average Rate of Change	x^3	$x^{3}$
51030	Find the Average Rate of Change	f(x)=-2e^(x+3)+2	$f (x) = - 2 e^{x + 3} + 2$
51031	Find the Average Rate of Change	f(x) = square root of 2x-9 from x_1=5 to x_2=8	$f (x) = \sqrt{2 x - 9}$ from $x_{1} = 5$ to $x_{2} = 8$
51032	Find the Average Rate of Change	x^2+3x	$x^{2} + 3 x$
51033	Find the Average Rate of Change	C(x)=100/(100-x)	$C (x) = \frac{100}{100 - x}$
51034	Find the Average Rate of Change	f(x)=(2x-1)/(x+3) ; [-10,-5]	$f (x) = \frac{2 x - 1}{x + 3}$ ; $[- 10, - 5]$
51035	Find the Average Rate of Change	y=3x^2	$y = 3 x^{2}$
51036	Find the Average Rate of Change	table[[x,f(x)],[-1,4/5],[0,4],[1,20],[2,100]]	$\begin{array}{c} x & f (x) \\ - 1 & \frac{4}{5} \\ 0 & 4 \\ 1 & 20 \\ 2 & 100 \end{array}$
51037	Find the Average Rate of Change	f(x) = square root of x+4	$f (x) = \sqrt{x} + 4$
51038	Find the Average Rate of Change	-(t-1)^2+5	$- {(t - 1)}^{2} + 5$
51039	Find the Average Rate of Change	g(x)=2/(x+3) over the interval 1<=x<=3 ?	$g (x) = \frac{2}{x + 3}$ over the interval $1 \leq x \leq 3$ ?
51040	Find the Average Rate of Change	3x^2+4	$3 x^{2} + 4$
51041	Find the Average Rate of Change	f(x)=(1/2)^x	$f (x) = {(\frac{1}{2})}^{x}$
51042	Find the Average Rate of Change	f(x)=1/x on 1 , 5	$f (x) = \frac{1}{x}$ on $1$ , $5$
51043	Find the Average Rate of Change	-2	$- 2$
51044	Find the Average Rate of Change	f(x)=0.04(8x-x^2)	$f (x) = 0.04 (8 x - x^{2})$
51045	Find the Average Rate of Change	V(t)=30(1.05)^3	$V (t) = 30 {(1.05)}^{3}$
51046	Find the Average Rate of Change	f(x)=x^4-8x^2+2 on -3 , 1	$f (x) = x^{4} - 8 x^{2} + 2$ on $- 3$ , $1$
51047	Find the Average Rate of Change	a(t)=1/(t+8)	$a (t) = \frac{1}{t + 8}$
51048	Find the Average Rate of Change	2y=5x+10	$2 y = 5 x + 10$
51049	Find the Average Rate of Change	f(x)=sin(x)	$f (x) = \sin (x)$
51050	Find the Average Rate of Change	y=1700(1.5)^(x/8)	$y = 1700 {(1.5)}^{\frac{x}{8}}$
51051	Find the Average Rate of Change	x^2+2x	$x^{2} + 2 x$
51052	Find the Average Rate of Change	f(x) = square root of 2x-1 from x_1=1 to x_2=3	$f (x) = \sqrt{2 x - 1}$ from $x_{1} = 1$ to $x_{2} = 3$
51053	Find the Average Rate of Change	f(x)=x-2 square root of x[1,9]	$f (x) = x - 2 \sqrt{x} [1, 9]$
51054	Find the Average Rate of Change	f(x)=2 square root of x	$f (x) = 2 \sqrt{x}$
51055	Find the Average Rate of Change	x^2-x-1	$x^{2} - x - 1$
51056	Find the Average Rate of Change	f(x)=x^3+x^2+x+2	$f (x) = x^{3} + x^{2} + x + 2$
51057	Find the Average Rate of Change	f(x)=x^2+2x-1 ;, [-3,-5/2]	$f (x) = x^{2} + 2 x - 1$ ;, $[- 3, - \frac{5}{2}]$
51058	Find the Average Rate of Change	f(x)=cos(x) , [0,pi/2]	$f (x) = \cos (x)$ , $[0, \frac{π}{2}]$
51059	Find the Average Rate of Change	f(x)=-2x^3+3x^2	$f (x) = - 2 x^{3} + 3 x^{2}$
51060	Find the Average Rate of Change	x^2+10x+20	$x^{2} + 10 x + 20$
51061	Find the Average Rate of Change	table[[x,y],[2,1],[2,2],[2,3]]	$\begin{array}{c} x & y \\ 2 & 1 \\ 2 & 2 \\ 2 & 3 \end{array}$
51062	Find the Average Rate of Change	y-73=-6(x-(-5))	$y - 73 = - 6 (x - (- 5))$
51063	Find the Average Rate of Change	f(x)=cot(x) , [(2pi)/3,(3pi)/2]	$f (x) = \cot (x)$ , $[\frac{2 π}{3}, \frac{3 π}{2}]$
51064	Find the Average Rate of Change	f(x)=5x^2-3 on [-2,5]	$f (x) = 5 x^{2} - 3$ on $[- 2, 5]$
51065	Find the Average Rate of Change	f(x)=x^3-5x-1 ; between 2 and 4	$f (x) = x^{3} - 5 x - 1$ ; between $2$ and $4$
51066	Find the Average Rate of Change	y = square root of x , (0,6)	$y = \sqrt{x}$ , $(0, 6)$
51067	Find the Average Rate of Change	f(x) = square root of x^3-4 , 2<=x<=5	$f (x) = \sqrt{x^{3} - 4}$ , $2 \leq x \leq 5$
51068	Find the Average Rate of Change	y=2x^2+3	$y = 2 x^{2} + 3$
51069	Find the Average Rate of Change	table[[x,y],[3,5],[10,p],[15,1],[30,0.5]]	$\begin{array}{c} x & y \\ 3 & 5 \\ 10 & p \\ 15 & 1 \\ 30 & 0.5 \end{array}$
51070	Find the Average Rate of Change	s(t) = square root of 2t , [2,8]	$s (t) = \sqrt{2 t}$ , $[2, 8]$
51071	Find the Average Rate of Change	n(p)=70-4p^2 ; 1<=p<=4	$n (p) = 70 - 4 p^{2}$ ; $1 \leq p \leq 4$
51072	Find the Average Rate of Change	-16t^2+50t+3	$- 16 t^{2} + 50 t + 3$
51073	Find the Average Rate of Change	f(x)=-3x^2+x+1[0,2]	$f (x) = - 3 x^{2} + x + 1 [0, 2]$
51074	Find the Average Rate of Change	f(x)=x^2+10[-2,-1]	$f (x) = x^{2} + 10 [- 2, - 1]$
51075	Find the Average Rate of Change	table[[x,Y],[-4,6],[0,4],[4,2],[8,0],[12,-2]]	$\begin{array}{c} x & Y \\ - 4 & 6 \\ 0 & 4 \\ 4 & 2 \\ 8 & 0 \\ 12 & - 2 \end{array}$
51076	Find the Average Rate of Change	f(x)=-2x^3+5x^2	$f (x) = - 2 x^{3} + 5 x^{2}$
51077	Find the Average Rate of Change	f(x)=-3x^3-6x^2+1x-4 on [3,8]	$f (x) = - 3 x^{3} - 6 x^{2} + 1 x - 4$ on $[3, 8]$
51078	Find the Average Rate of Change	f(x)=2x^2-2x-1 ; [1,3/2]	$f (x) = 2 x^{2} - 2 x - 1$ ; $[1, \frac{3}{2}]$
51079	Find the Average Rate of Change	h(x)=9-2x	$h (x) = 9 - 2 x$
51080	Find the Average Rate of Change	f(t)=21t-3t^2 ; 0<=t<=9	$f (t) = 21 t - 3 t^{2}$ ; $0 \leq t \leq 9$
51081	Find the Average Rate of Change	table[[x,y],[1,2],[2,2/5],[3,2/25],[4,2/125]]	$\begin{array}{c} x & y \\ 1 & 2 \\ 2 & \frac{2}{5} \\ 3 & \frac{2}{25} \\ 4 & \frac{2}{125} \end{array}$
51082	Find the Average Rate of Change	f(x)=2x^2+8 over the interval [2,6]	$f (x) = 2 x^{2} + 8$ over the interval $[2, 6]$
51083	Find the Average Rate of Change	f(t)=1-2t+4t^2	$f (t) = 1 - 2 t + 4 t^{2}$
51084	Find the Average Rate of Change	f(x)=-(x^2)/4+7	$f (x) = - \frac{x^{2}}{4} + 7$
51085	Find the Average Rate of Change	f(x)=4x^3-5x-2 ; between 1 and 3	$f (x) = 4 x^{3} - 5 x - 2$ ; between $1$ and $3$
51086	Find the Average Rate of Change	f(x)=( square root of x^2-1)/x , 1<=x<=7	$f (x) = \frac{\sqrt{x^{2} - 1}}{x}$ , $1 \leq x \leq 7$
51087	Find the Average Rate of Change	f(x)=3x , [1,4]	$f (x) = 3 x$ , $[1, 4]$
51088	Find the Average Rate of Change	f(x)=x+1	$f (x) = x + 1$
51089	Find the Average Rate of Change	f(x)=(2x-1)/(3x+5)	$f (x) = \frac{2 x - 1}{3 x + 5}$
51090	Find the Average Rate of Change	y=(1.06)^(8t)	$y = {(1.06)}^{8 t}$
51091	Find the Average Rate of Change	f(x)=1/(2x)	$f (x) = \frac{1}{2 x}$
51092	Find the Average Rate of Change	r(a)=5a	$r (a) = 5 a$
51093	Find the Average Rate of Change	9x-11y+2=0 ?	$9 x - 11 y + 2 = 0$ ?
51094	Find the Average Rate of Change	f(x) = square root of 3x-5 from x_1=2 to x_2=4	$f (x) = \sqrt{3 x - 5}$ from $x_{1} = 2$ to $x_{2} = 4$
51095	Find the Average Rate of Change	f(x) = square root of 2x-3 from x_1=2 to x_2=5	$f (x) = \sqrt{2 x - 3}$ from $x_{1} = 2$ to $x_{2} = 5$
51096	Find the Average Rate of Change	table[[x,y],[0,5],[1,10],[2,15],[3,20],[4,25],[5,30]]	$\begin{array}{c} x & y \\ 0 & 5 \\ 1 & 10 \\ 2 & 15 \\ 3 & 20 \\ 4 & 25 \\ 5 & 30 \end{array}$
51097	Find the Average Rate of Change	f(x)=0.5(-10x+24)	$f (x) = 0.5 (- 10 x + 24)$
51098	Find the Average Rate of Change	y=x^3+x^2-8x-7	$y = x^{3} + x^{2} - 8 x - 7$
51099	Find the Average Rate of Change	f(x)=14+2e^(-2x)	$f (x) = 14 + 2 e^{- 2 x}$
51100	Find the Average Rate of Change	y=- square root of x-1+5	$y = - \sqrt{x - 1} + 5$