AP Calculus AB Jeopardy!

Differentiation 1

100

Find the derivative of f(x)=3/2x²

What is 3x?

200

Find the derivative of 7x³+9x²+5x

What is 21x²+18x+5?

300

Find the slope of f(x)=5/3x³-3x²-1/x² at x=-1

What is 9?

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?

500

Set up the derivative of f(x)=3x²-2 using the difference quotient and limits.

What is the limit as h approaches 0 of

[3(x+h)^2-2- (3x^2-2)]/h

Differentiation 2

100

Find dy/dx. xy²+y³+x²=10

What is (-2x-y²)/(2xy+3y²)?

200

Find the derivative of f(x)=ln(x³+3x²+7).

What is (3x²+6x)/(x³+3x²+7)?

300

Find dy/dx for the following function: x²y³+y²+3x=y.

What is (-3-2xy³)/(3x²y²+2y-1)?

400

Find the derivative of f(x)=tan(3x).

What is 3sec²(3x)

500

Solve for d²y/dx² when y²=3x²+4x+y at the point (2,5).

What is -.036?

Anti-differentiation

100

Integrate F'(x)=3x²+6x.

What is x³+3x²+C?

200

Integrate F'(x) = x²

What is (x³/3 +C

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

400

Solve for y=f(x) when f(3)=2. dy/dx=x²+3x/y²

What is (2/3x³+2x²-32)^.5?

500

Integrate x/(4+x²)^.5.

What is (4+x²)^.5+C?

Theorems

100

Complete the Fundamental Theorem of Calculus. ∫_a^bF(x)dx=?

What is F(b)-F(a)?

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)?

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 2/(3)^.5?

400

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

What is 9x+9?

500

Find F'(x), if F(x)=∫_-3^x(7t+9)dt.

What is 7x+9?

Applications

100

Find the area of the region bounded by f(x)=x²-3x-10 and g(x)=-x²+5x+14.

What is 170.667?

200

Find the average acceleration of a particle over the interval (0,50) given v(50)=80ft/sec and an initial velocity of 10 ft/sec. Include units in your answer.

What is 7/5 ft/sec²?

300

The rate of change of radius r of a circle is 4 cm/s. Find the rate of change of Area A when r=2cm.

What is 16π?

400

The acceleration of a particle is given by the function a(t)=3t²+7. Find the position function of the particle given that its initial velocity is 10 m/sec and an initial height of 80m.

What is s(t)=(t⁴/4)+3.5t²+10t+80?

500

Find the volume of the solid generated by revolving the region bounded by y=x², the x-axis, and x=2 around the y-axis.

What is 8π?