TMUA · Paper 1: Applications of Mathematical Knowledge

Differentiation

13 practice questions, each with the answer and an explanation.

Practise Differentiation now

Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 13 questions

What is the local maximum value of $f (x) = x^{3} - 6 x^{2} + 9 x$ ?
What is the gradient of the curve $y = x^{3} - 3 x$ at the point where $x = 2$ ?
The tangent to $y = x^{2}$ at the point where $x = 3$ crosses the $x$ -axis at $(p, 0)$ . What is $p$ ?
The normal to the curve $y = x^{2} + 1$ at the point $(1, 2)$ crosses the $y$ -axis at $(0, c)$ . What is $c$ ?
The curve $y = x^{3} + a x^{2} + b$ has a stationary point at $x = 2$ . What is $a$ ?
The function $f (x) = x^{3} - 3 x^{2} + k$ has a local minimum value of $0$ . What is $k$ ?
What is the maximum value of $12 x - x^{3}$ for $x \geq 0$ ?
A square sheet of card has side $12$ cm. A square of side $x$ cm is cut from each corner and the sides are folded up to make an open box. What is the greatest possible volume of the box, in cm $^{3}$ ?
How many stationary points does the curve $y = x^{4} - 4 x^{3}$ have?
What is the minimum value of $x + \frac{4}{x}$ for $x > 0$ ?
For which values of $x$ is $f (x) = 2 x^{3} - 9 x^{2} + 12 x$ increasing?
The curve $y = a x^{2} + b x$ passes through $(1, 5)$ and has gradient $7$ at that point. What is the value of $ab$ ?
The cubic $y = x^{3} - 3 x^{2} - 9 x + k$ has exactly two distinct real roots for some positive value of $k$ . What is that value of $k$ ?

Keep practising

More TMUA topics

All TMUA practice →

Differentiation in other exams

Ready for the full TMUA test?

Take a mock test TMUA hub