AP Calculus AB Jeopardy!

Differentiation 1

100

Find the derivative of f(x)=10ln(2x)

What is 10/x?

200

Find the derivative of -9.33cos(x).

What is 933sin(x)/100?

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

Find the derivative of f(x)=3x²+7x-2 using the limit process.

What is 6x+7?

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

What is the particular solution to the differential equation dy/dx=9x(3)/e with the initial condition y(0)=1?

What is y=(27x^2)/(2e)-(329.271)?

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

Using the Fundamental Theorem of Calculus, what is∫_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

Define the Mean Value Theorem.

What is a theorem that states that if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f'(c) is equal to the function's average rate of change over [a,b]?

400

Define the Extreme Value Theorem.

What is a theorem that guarantees both a maximum and minimum value for a function under such conditions: It states the following: If a function f(x) is continuous on a closed interval [ a, b], then f(x) has both a maximum and minimum value on [ a, b]?

500

Use the second Fundamental Theorem of Calculus to find F'(x). F(x)=∫_-3^x(7t+9)dt.

What is 7x+9?

Applications

100

Determine the area of the region bounded by f(x)=xe^(x^2), y=x+1, x=2, and the y=axis.

What is 3.5092?

200

Find the area under the curve f(x)=9.1sin(x) on the interval [0, 2pi].

What is 36.4?

300

Find the volume for solid of revolution between the curves y=2.3x+1, y=0.1e, and x=2.5 around the x-axis.

What is 139.364?

400

Suppose an object’s velocity is given by v(t)=e^1.2t+sin(0.9t). Calculate the displacement of the object from t=1 to t=9.6.

What is 83923.678 units?

500

Find the equation of the line tangent to f(x)=1.23x^1.5+2x at x=0.

What is y=2x?