AB Calculus Jeopardy

Derivatives

100

D/dx Sin = ?

Cosx

200

D/dx e^x = ?

e^x

300

D/dx tanx = ?

sec^2x

400

D/dx csc = ? 

-cscxcotx

500

If f and g are inverses, then g'(x) = ?

1/f'(g(x))

Anti-derivatives

100

Integral of sinxdx = ?

-cosx + C

200

Integral of secxtanxdx = ? 

secx + C

300

Integral of a^x dx = ? 

(a^x/lna) + C

400

Integral of e^{x dx= ?} 

e^x + C

500

Integral of 1/(x^2)+1 dx = ?

tan^(-1)x + C

Theorems

100

What is the ONE condition needed to fulfill the Extreme Value Theorem? 

Continuous

200

What TWO Conditions must be met for the Mean Value Theorem? 

Continuous

Differentiable

300

What is a brief definition of the Rolle's theorem

If f(a) and f(b) are the same, the slope of f(c) must equal 0.

400

What is the formula for the Mean Value Theorem

f'(c) = f(b) - f(a) / b - a

500

Which theorems MUST be CONTINUOUS 

Rolles, MVT, EVT, IVT

Graphical Analysis

100

What happens to f when f' is greater than 0?

f is increasing. 

200

What does a function have when f'(x) = 0 and changes from DECREASING to INCREASING? 

A relative minimum

300

For the equation -2x^3 + 6x + 5, find the critical numbers that are less than 0. 

-1

400

If a function's slope is positive, will a right reimann sum be an over or underestimate? 

Overestimate. 

500

If f'(x) is decreasing, what is the quality of the function's concavity? 

It is negative. 

Pos, Vel, Acc

100

If the velocity of a particle is positive, in what directions could the particle be moving? (Hint: It is literally an incredibly simple question)

Up or to the right. 

200

The formula for average velocity (given POSITION) is = ? 

x(b)-x(a)/b-a

300

How do displacement and distance differ? 

Distance is calculated with an absolute value while displacement is not. 

400

What happens to a particle's movement when velocity switches from positive to negative

It switches from going right to left or from going up to down. 

500

If acceleration and velocity are both negative, is a particle speeding up or slowing down?

Speeding up.