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?

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).

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?

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?

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

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?

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.

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

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?