AP Calc Review

Derivatives

100

f(x) = 4x³+2x²+x+5

find f'(x)

f'(x)= 12x²+4x+1

200

Find the derivative using the product rule in simplest form.

f(x)= (x²-1)(x+5)

f'(x) = 3x² +10x -1

300

What is the acceleration of the following function, at t=2.

x(t)= 3t³+4t² -2t + 16

44

400

Find the derivative of the following:

f(x)= (x+2)/(3x+1)

f'(x) = -5/(3x+1)²

500

Find the derivative using implicit differentiation:

e^2y=3x

dy/dx = 3/2e^2y

Integrals

100

Integrate the following: 

∫(6x²-4x+5) dx

f(x) = 2x³-2x²+5x+c

200

Integrate the following:

∫e ^5x dx

e^5x/5 + c

300

If f'(x) = 20x³ + 2, find f(x) if the point (1,2) is on the curve

f(x)= 5x⁴+2x-5

400

Integrate the following (hint: natural log):

∫ x²/ (1 + x³) dx

1/3 ln l1 + x³l + c 

500

Integrate the following using u substitution:

∫sin² x cos x dx 

1/3 sin³x + c

Limits/Asymptotes

100

Refer to the graph on board:

What is the value of f(5)

f(5) = 2

200

Refer to the graph on board:

At what letter(s) is there a removable discontinuity?

A,C

300

Refer to the graph on the board:

At what letter(s) is there a jump discontinuity?

B

400

What is the horizontal asymptote of the function.

f(x)= 4x - 1 / 3 - 2x

y = -2

500

Find the limit:

                                3x⁵ - 2x³+ 21

lim x  --> ∞    ____________________

                               6x³ + 2x + 1

∞  

FUN Chart

100

If f(x) is increasing is f'(x) positive or negative

Positive

200

If f(x) is concave down, is f''(x) positive or negative?

Negative 

300

If f(x) has a turning point at x = 6, what is the value of f'(6)?

f'(6) = 0

400

If f''(2) is crossing the x-axis what is f(2)?

A. Horizontal Asymptote

B. Vertical Asymptote

C. Inflection Point

D. None of the Above

C. An inflection point

500

The graph of y = 3x⁵ - 10x⁴ has an inflection point at 

(2, -64) 

Random

100

Find f(x) of the following: 

                         2(x+ h)⁵ - 5(x+h)³ - 2x⁵ + 5x³

  ^{lim h --> 0                 _________________________________}

                                                          ^h

f(x)= 2x⁵ - 5x³

200

Find the equation of the tangent line to f(x)= 3x²-x   at x=1

y - 2= 5 (x-1)

or y= 5x -3 

300

Find f'''(x) in simplest form.

f(x)= 2/3x⁴+1/6x⁶-5/6x³

f'''(x)= 16x + 20x³ - 5

400

Find the value for the constant "k" that will make the function continuous.             

             

                   x², x<2

 f(x) =         k - x, x ≥ 2

k = 6

500

A particle moves along the x - axis with velocity given by v(t) = 3t² + 8t for time t≥o if the particle is at x = -3, at time t=2, find the position at t= 1. 

x(1) = -22