Differentiation 1
Differentiation 2
Anti-differentiation
Theorems
Applications
100
Find the derivative of f(x)=3/2x2
What is 3x?
100
Find dy/dx. xy2+y3+x2=10
What is (-2x-y2)/(2xy+3y2)?
100
Integrate F'(x)=3x2+6x.
What is x3+3x2+C?
100
Complete the Fundamental Theorem of Calculus. ∫abF(x)dx=?
What is F(b)-F(a)?
100

The average rate of change of f(x) on [2, 5] is 4.  Find the area of the region between the curve of f(x), the x-axis, and the vertical lines x = 2 and x = 5.

What is 12?

200
Find the derivative of 7x3+9x2+5x
What is 21x2+18x+5?
200
Find the derivative of f(x)=ln(x3+3x2+7).
What is (3x2+6x)/(x3+3x2+7)?
200
Integrate F'(x) = x2
What is (x3/3 +C
200
What does the Mean Value Theorem state?
What is there exists a point c in the interval (a,b) such that f'(c)=f(b)-f(a)/b-a, if a function is continuous on the closed interval [a,b] and differentiable on the open interval (a,b)?
200

Find the average velocity of a particle over the interval (0, 5) given v(t)= 8t ft/sec.

What is 20 ft/sec?
300
Find the slope of f(x)=5/3x3-3x2-1/x2 at x=-1
What is 9?
300
Find dy/dx for the following function: x2y3+y2+3x=y.
What is (-3-2xy3)/(3x2y2+2y-1)?
300
Find the equation of F given F'(x)=x3-3x2+7x+8 and F(0)=5
What is F(x)=(x4/4)-x3+3.5x2+8x+5
300
Find a value c such that the conclusion of the mean value theorem is satisfied for f(x)=2x,3+6x-2 on the interval [-2,2].
What is &plusmn 2/(3).5?
300

If the velocity of a particle is  v(t) = 8/(t2 + 5)  and the position of the particle at t = 3 is x(3) = 5, what is x(10)?  [CALCULATOR ACTIVE]

What is 6.5045?

400

Find the derivative of f(x)=(x+3)3/(x-2)2 - x2(7x+7)

What is (x+3)2[3(x-2)-2(x+3)]/(x-2)3-21x2-14x?

400
Find the derivative of f(x)=tan(3x).
What is 3sec2(3x)
400

Solve for y=f(x) when f(3)=2. dy/dx=x2+3x

What is (x3/3 + 3x2/2 - 20.5)?

400
Use the second Fundamental Theorem of Calculus to find F'(x). F(x)=∫2x(9t+9)dt.
What is 9x+9?
400

If the rate of water flowing into a pool is given by W(t) = 3 + tsin(3t2), in gallons per minute, find the amount of water that enters the pool in the first 5 minutes.  [CALCULATOR ACTIVE]

What is 15.013 gallons?

500
If x = 3, find limx->2 (((x+h)2+2) - (x2+2)) / h

What is 6?

500
Solve for d2y/dx2 when y2=3x2+4x+y at the point (2,5).
What is -.036?
500
Integrate x/(4+x2).5.
What is (4+x2).5+C?
500
Use the second Fundamental Theorem of Calculus to find F'(x). F(x)=∫-3x(7t+9)dt.
What is 7x+9?
500

A particle has acceleration a(t) = -2cos(2t).  If v(0) = 5 and x(0) = 1, find x(t).

What is 0.5cos(2t) + 5t + 0.5

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