Calculus Challenge

What is the derivative of f(x) = 3x^2 + 2x - 5?

• f'(x) = 3x^2 + 2

• f'(x) = 6x - 2

• f'(x) = 3x^2 + 2x - 5

• f'(x) = 6x + 2

Which rule is used to find the derivative of a product of two functions?

• Quotient Rule

• Product Rule

• Chain Rule

• Power Rule

What is the definite integral of f(x) = 4x^3 + 2x^2 - 3x + 1 from 0 to 2?

• 28 + 16/3

• 28 + 16/2

• 28 + 16/4

• 28 + 16/5

In which situation would you use L'Hopital's Rule?

• When simplifying algebraic expressions

• When solving systems of linear equations

• When finding the derivative of a function

• When evaluating limits resulting in indeterminate forms

What is the area under the curve y = x^2 from x = 0 to x = 3?

• 9

• 15

• 12

• 6

What is the limit of (sin(x) / x) as x approaches 0?

• 2

• 1

• 0

• π

What is the second derivative of f(x) = 5x^4 - 3x^2 + 2x?

• f''(x) = 10x^4 - 3x^2 + 2

• f''(x) = 30x^3 - 6

• f''(x) = 60x^2 - 6

• f''(x) = 20x^2 - 3

What is the slope of the tangent line to the curve y = 2x^3 - x at the point (1, 1)?

• 5

• 10

• 3

• 7

What is the antiderivative of e^x?

• e^x - C

• e^x * C

• e^(x^2)

• e^x + C

When is the Mean Value Theorem applicable?

• The Mean Value Theorem is applicable when the function is differentiable on a closed interval.

• The Mean Value Theorem is applicable when the function is continuous on a closed interval and differentiable on the open interval.

• The Mean Value Theorem is applicable when the function is continuous on an open interval.

• The Mean Value Theorem is applicable when the function is discontinuous on a closed interval.