Calculus Derivatives and Integrals Quiz

Find the derivative of f(x) = 7x³ - 4x² + 2x - 9.

• 21x² - 8x + 2

• 21x² - 8x + 2x - 9

• 7x² - 4x + 2

• 21x - 8 + 2

What is the slope of the tangent line to g(x) = x⁴ - 5x² + 2 at x = 1?

• -6

• 6

• -10

• 10

Find the derivative of h(x) = sin(4x).

• 4cos(4x)

• cos(4x)

• 4sin(4x)

• -4cos(4x)

What is the integral of ∫ (3x² + 5x - 2) dx?

• 6x + 5 + C

• x³ + (5/2)x² - 2x + C

• 3x³ + 5x² - 2x + C

• 9x⁴ + 25x² - 2x + C

Evaluate the definite integral ∫₁³ (x² + 2) dx.

• 10

• 11

• 12

• 14

Find the derivative of f(x) = e^(−x).

• e^(−x)

• -e^(−x)

• xe^(−x)

• e^x

What is the derivative of y = ln(5x)?

• 1/x

• 5/x

• 1/(5x)

• 5/(5x) = 1/x

Find the critical points of f(x) = x³ - 6x² + 9x + 2.

• x = 1, x = 3

• x = 0, x = 3

• x = 1, x = 0

• x = 0, x = 1, x = 3

If a ball is thrown upward with an initial velocity of 64 ft/s, its height (in feet) after t seconds is given by h(t) = 64t - 16t². What is the maximum height?

• 64 ft

• 128 ft

• 32 ft

• 16 ft

Find the limit: lim (x² - 9) / (x - 3) as x approaches 3.

• 0

• 6

• 9

• Undefined