AP Review

What is the limit?

• DNE
• Infinity
• 6
• 12

Find the limit as x approaches 3 from the left

• 4
• 3
• 2
• DNE

• A
• B
• C
• D

Find the second derivative of the function:
f (x) =  2x - 5x⁶

• f ''(x)= 2 - 30x
• f ''(x) =  2-30x⁵
• f ''(x) = -30x⁵
• f ''(x) = -150x⁴

Find the derivative of the given equation
f(x) = 1/x²

• 1/2x
• -2x
• 2x
• -2x^-3

Find the derivative
f(t) = (t² + 2t)⁵

• f'(t) = 5(2t+2)⁴
• f'(t) = 5(t² + 2t)⁴
•  f'(t) = 5(t² + 2t)⁴(2t)
• f'(t) = 5(t² + 2t)⁴(2t + 2)

Find the second derivative of
f(x) = x² + e^x  - cosx

• f"(x) = 2 + e^x + cosx
• f"(x) = 2x + e^x + cosx
• f"(x) = 2x + xe^x - cosx
• f"(x) = 2x + e^x + sinx

Find the derivative.
 f(z) = 1/(3z²) + 4z³

• f'(z) = 6z³ + 12z²
• f'(z) = 6z + 12x²
• f'(z) =  -2/(3z³) + 12z²
• f'(z) = -6/z² + 12z²

The graph of y = 3x² - x³ has a relative maximum at

• (2, 4) only
• (0, 0) only
• (0, 0) and (2, 4)
• (1, 2)

The function f is twice differentiable with f(2) = 1, f'(2)=4, and f''(2)=3.  What is the value of the approximation of f(1.9) using the line tangent to the graph of f at x = 2?

• 0.4
• 0.6
• 0.7
• 1.4