3. Differentiation

Differentiation Basics — Quiz

Test your understanding of differentiation basics with 5 practice questions.

Practice Questions

Question 1

A particle moves along a straight line such that its displacement $s$ (in meters) from the origin at time $t$ (in seconds) is given by $s(t) = 2t^3 - 15t^2 + 24t - 7$. At which time(s) is the particle momentarily at rest?

Question 2

The gradient of the tangent to the curve $y = x^3 - 6x^2 + 10x - 3$ at a certain point is $1$. Find the x-coordinate(s) of this point.

Question 3

Given that $f(x) = ax^3 + bx^2 + c$ and $f'(x) = 6x^2 + 8x$, and $f(1) = 5$, find the value of $c$.

Question 4

The normal to the curve $y = x^2 - 5x + 2$ at the point where $x = 3$ has a gradient of:

Question 5

For the function $f(x) = x^3 - 12x + 1$, find the x-coordinates of the stationary points.