Cumulative Review

At which point(s) will the slopes of the tangent line are zero?

• at C only

• at points A, C and E only

• at point B and D only

• at points A and E only

Given f(x) = ax² + 2bx. What are a and b if f'(x) = 8x + 6?

• a = 2 and b = 3

• a = 3 and b = 2

• a = 3 and b = 4

• a = 4 and b = 3

At what point will the slope of y = -x² + 4 is zero?

• (0, 4)

• (1, 4)

• (4, 0)

• (1, 0)

What is the slope of the line normal to the curve y = x² + x at x = 1?

• -1

• -1/2

• -1/3

• -1/4

What is the equation of the line tangent to the curve y = x² at x = 1?

• y = 2x + 1

• y = 2x - 1

• y = -2x + 1

• y = x - 1

What is the derivative of f?

• 1/(x - 1)^-1

• -1/(x - 1)^-2

• -1/(x - 1)

• -1/(x - 1)²

Let y = x³ - 3x. At what value of x will the rate of change is zero? Choose the best answer.

• at x = 0 only

• at x = -1 only

• at x = 1 only

• at x = -1 or x = 1 only

What is the equation of the line tangent to the curve y = -x² + 3 at (1, 2)?

• y = 2x - 4

• y = -2x - 4

• y = -2x + 4

• y = 2x + 4

What is the derivative of y = 2π?

• 0

• 2

• -2

• None of the above

What is the rate of change of f(t) = 2t³ - 4t + 1 when t = 2s and f is in meter (m)?

• 16 m/s

• 20 m/s

• 24 m/s

• 30 m/s