AP Calc Review (1st semester)

What is the integral of sec²x?

• tanx
• tanx + C
• secxtanx + C
• secxtanx

• A
• B
• C
• D

Find the derivative. f(x) = 1/(3x²) + 4x³

• f'(x) = 6x³ + 12x²
• f'(x) = 6x + 12x²
• f'(x) =  -2/(3x³) + 12x²
• f'(x) = -6/x² + 12x²

If the position of a particle is represented by s(t) = -t² + 1, what is its instantaneous velocity at t = 1?  

• Velocity = 0
• Velocity = 1
• Velocity = -1
• Velocity = -2

Find the slope of the tangent line to f(x) = -3x²-6x at x = 1.

• m = 0
• f'(x) = -6x - 6
• f'(x) = 6x
• m = -12

If the position function for a particle is s(t) = -t² - t, what is the instantaneous velocity function for the particle?

• v(t) = -2

• v(t) = -2t - 1

• v(t) = t³

• v(t) = -t

Find the derivative f(x) = (3x + 5)⁴

• f'(x) = 12(3x)³
• f'(x) = 12(3x + 5)³
• f'(x) = (3)⁴
• f'(x) = (3x + 5)³

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

Where does the function, f(x) = 2x³ - 9x² + 12x -3 have relative max/min?

• Rel max x = -1, Rel min x = 2
• Rel min x = 1, Rel min x = 2
• Rel max x = 1, Rel min x = 2
• Rel max x = 2, Rel min x = 1

Find the derivative f(x) = xe^x

• f'(x) = e^x

• f'(x) = xe^x + xe^x

• f'(x) = e^x - xe^x

• f'(x) = e^x + xe^x

Tags

CCSS.HSF.IF.A.2

CCSS.HSF.IF.C.8