Calculus Quiz

What is the absolute maximum value of the function f(x) = x³ - 3x² + 2 on the interval [-1, 3]?

• 2

• 4

• 6

• 8

Which of the following is a critical point of the function f(x) = x⁴ - 8x² + 2?

• x = 0

• x = 2

• x = -2

• All of the above

On what interval is the function f(x) = x³ + 3x² - 9x + 5 increasing?

• (-∞, -3)

• (-3, 1)

• (1, ∞)

• (-∞, -3) U (1, ∞)

On what interval is the function f(x) = x⁴ - 4x³ + 6x² - 4x + 1 concave up?

• (-∞, 1)

• (1, ∞)

• (-∞, ∞)

• None of the above

The Mean Value Theorem for a function f(x) on the interval [a, b] states:

• There exists a c in (a, b) such that f'(c) = (f(b) - f(a))/(b - a)

• f(x) is continuous on [a, b]

• f(x) is differentiable on (a, b)

• All of the above

Which of the following conditions is necessary to apply L'Hopital's Rule?

• The limit must be in an indeterminate form

• The function must be continuous

• The function must be differentiable

• a and c

What is the antiderivative of the function f(x) = 2x?

• x² + C

• x²/2 + C

• 2x + C

• 2

Which of the following is the equation of the horizontal asymptote of the graph of f(x) = (3x² - 2x + 1)/(x² + 1)?

• y = 0

• y = 1

• y = 3

• There is no horizontal asymptote

Which of the following functions has an inflection point at x = 0?

• f(x) = x³

• f(x) = x⁴

• f(x) = x²

• f(x) = x

What is the derivative of the function f(x) = sin(x²)?

• 2x cos(x²)

• cos(x²)

• -2x cos(x²)

• -cos(x²)