IBDP Calculus Differentiation Quiz

Andy is working on a project to calculate the derivative of a function. What is the derivative of the function f(x) = 3x² + 2x - 5?

• f'(x) = 3x² + 2x - 5

• f'(x) = 6x - 2

• f'(x) = 3x² + 2

• f'(x) = 6x + 2

William is working on a project involving the curve y = 2x³ - 3x² + 4x - 1. He needs to find the equation of the tangent line to the curve at the point (1, 2).

• y = 5x - 3

• y = 3x + 1

• y = 2x² + 4x - 1

• y = 4x - 2

If the speed of a car is increasing for all time during a journey from point A to point B, what can be said about the car's motion during that journey?

• The car's motion is increasing throughout the journey from point A to point B.

• The car's motion is undefined during the journey from point A to point B.

• The car's motion is constant during the journey from point A to point B.

• The car's motion is decreasing during the journey from point A to point B.

Michelle is working on a project to calculate the derivative of a function. What is the derivative of the function g(x) = 4x⁴ - 6x³ + 5x² - 2x + 3?

• g'(x) = 16x³ - 18x² + 10x + 2

• g'(x) = 12x³ - 14x² + 8x - 2

• g'(x) = 8x³ - 9x² + 5x - 2

• g'(x) = 16x³ - 18x² + 10x - 2

Ruby is trying to determine the equation of the normal line to the curve y = x³ - 2x² + 3x + 1 at the point (2, 3).

• y = 2x + 5

• y = -x + 2

• y = 4x - 7

If the second derivative of a function f(x) is negative for all x in the interval (c, d), what can be said about the function f(x) in that interval?

• Increasing

• Concave up

• Constant

• Concave down

Sahil is finding the rate of change of the profit function P(x) = 5x⁵ - 4x⁴ + 3x³ - 2x² + x - 1, with respect to the number of units sold.

• P'(x) = 25x⁴ - 14x³ + 9x² - 4x + 1

• P'(x) = 25x⁴ - 16x³ + 6x² - 4x + 1

• P'(x) = 20x⁴ - 16x³ + 9x² - 4x + 1

• P'(x) = 25x⁴ - 16x³ + 9x² - 4x + 1

Cyrus wants to determine the equation of the tangent line to the curve y = 3x² - 2x + 1 at the point (0, 1).

• y = -2x + 1

• y = 4x - 1

• y = 2x + 1

• y = 3x² - 2x + 1

If the speed of a car is constant for some time interval (p, q), what can be said about the distance covered by the car during that time?

• The distance covered by the car is always decreasing during that time.

• The distance covered by the car is undefined during that time.

• The distance covered by the car is always increasing during that time.

• The distance covered by the car has a constant rate during that time.

Aviva wants to find the derivative of the revenue function for her business, which is given by R(x) = 2x³ - 5x² + 4x - 7. What is the derivative of the revenue function?

• R'(x) = 6x² - 10x + 4

• R'(x) = 6x² - 5x + 4

• R'(x) = 6x³ - 10x² + 4x

• R'(x) = 2x³ - 5x² + 4x - 7