AP Calculus AB Jeopardy!

Differentiation 1

100

Find the derivative of f(x)=1.5x²

What is 3x?

200

Find the derivative of 7x³+9x²+5x

What is 21x²+18x+5?

300

Find the slope of f(x)=3x³-3x²-x^-2 at x=-1

What is 13?

400

Find the derivative of f(x) = arctan x

What is 1 / (1 + x^{2) ?}

500

Find the derivative of f(x) = 2^x

What is (ln 2) 2^{x ?}

Miscellaneous

100

Find dy/dx. xy²+y³+x²=10

What is (-2x-y²)/(2xy+3y²)?

200

The limit as x approaches 0 of (cos x - 1) / x

What is 0?

300

Write the equation for the line tangent to g(x)=2/(x^{3) where x=2.}

y - 1/4 = -3/8 (x-2)

400

Find a value for b so that the piecewise function k(x) is continuous k(x) = (16-x^2)/(20+5x), x does not equal -4 b(x+2), x=-4

b=-4/5

500

What is the slope of the tangent line to y = (3x-5)/(2x-3) at x=0?

Slope is 1/9

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

Water is pumped out of a holding tank at a rate of 5 - 5e^(-0.15t) liters/minute, where t is in minutes since the pump is started. If the holding tank contains 1000 liters of water when the pump is started, how much water does it hold one hour later?

Whst is 733.329?

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.

300

Find a value c such that the conclusion of the mean value theorem is satisfied for f(x)=2x³+6x-2 on the interval [-2,2].

What is &plusmn 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). F(x)=∫_-3^x2(7t+9)dt.

What is 7x+9?

Applications

100

The function y=x⁴+bx²+8x+1 has a horizontal tangent and a point of inflection for the same value of x. What must be the value of b?

What is -6?

200

Find the average acceleration of a particle over the interval (0,5) given v(t)=t+6t²

What is 31?

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

Let f(x) = (15)x² Find the average value of f on [1,2].

What is 35/3?