Scottish Highers · Higher Mathematics

Differentiation, Stationary Points and Curve Sketching

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

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

All 6 questions

Differentiate $f (x) = \frac{3 x ^{4} - 2 x ^{2} + 5}{x}$ with respect to $x$ for $x \neq = 0$ .
Find the coordinates of the turning points of the curve $y = 2 x^{3} - 3 x^{2} - 12 x + 4$ .
The displacement of an object is given by $s (t) = t^{3} - 6 t^{2} + 9 t + 2$ . At what times $t \geq 0$ is the object instantaneously at rest?
Find the rate of change of the volume of a cube with side length $x$ with respect to its surface area $A$ .
A rectangular garden is to be fenced on three sides using $40 m$ of fencing, with an existing wall forming the fourth side. What is the maximum possible area of the garden?
The curve $y = x^{3} + a x^{2} + b x + c$ has a stationary point of inflection at $(2, 5)$ . What are the values of $a$ and $b$ ?

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