Find the average value of the function f(x)=x^3-3x^2 on the interval [-2,1].
What is -17/4
100
Find the average rate of change for the function
f(x)=3x-x^2 on the interval [1,3]
What is -1
200
Quotient Rule
What is (g(f`)-f(g`))/g^2
200
fnInt(1/x+2)
What is ln(abs(x))+2x+C
200
f(x)=ln(2x^2+6x+8)
What is f`(x)=(4x+6)/(2x^2+6x+8)
200
If A=(pi)r^2, find dA/dt when r=2 and dr/dt=3.
What is dA/dt=12(pi)
200
Find the equation of the tangent line to the graph
f(x)=x^3+3x^2+6x at the point x=2
What is y=24x-16
300
Shell Method
What is V=2(pi) fnInt(x(f(x)),x,a,b)
300
fnInt(1/(1+x^2))
What is arctanx+C
300
f(x)=6^x
What is f`(x)=(6^x)(ln(6))
300
Find the area bound between the graphs f(x)=x^2-2x and g(x)=2x
What is 32/3 units^2
300
Find a point for the graph of f(x)=3x^2+x-4 on the interval [1,5] that satisfies the mean value theorm
What is x=3
400
The Limit Definition of the Derivative
What is lim(h->0) (f(x+h)-f(x))/h
400
fnInt(x(x^2+1)^3)
What is ((x^2+1)^4)/4+C
400
f(x)=tan(3x^2)
What is f`(x)=6xsec^2(3x^2)
400
A solid is 12 inches high. The cross-section of the solid at height x above its base has an area of 3x square inches. Find the volume of the solid.
What is 216 inches^3
400
Find the horizontal and vertical asymptotes of the graph of f(x)=(4x)/(x^2-1)
What is x=-1,1 vertical and y=0 horizontal
500
Integration by parts *After AP Exam (omit if before)
What is fnInt(u(dv))= u(v) - fnInt(v(du))
500
fnInt((ln(x))^2(1/x)) *After AP Exam (omit if before)
What is (ln(x))^3/3+C
500
f(x)=arcsin(2x)
What is f`(x)=2/(squareroot(1-4x^2))
500
Each side of a cardboard square is 12 inches. What is the maximum volume of a box that can be made from the square by cutting congruent squares from the corners and turning up the 4 sides?
What is 128 in^3
500
Find a solution to the differential equation dy/dx=2ycos(x) that satisfies the initial condition y(pi)=5