Edexcel IGCSE Math B 4.M rates of change and stationary points

Practise rates-of-change questions by differentiating or using graph gradients, then solving for stationary points or parameter values.

Exam points

Use differentiation or gradient reasoning to locate stationary points on a curve.
Solve derivative equations to find turning-point coordinates to the required accuracy.
Use maximum or minimum information to find unknown constants in a curve equation.

[Maximum number: 4]

Figure for Question 4.M Rates of change and stationary points question 1 — Edexcel IGCSE Math B

Diagrams NOT accurately drawn.

Figure 3 shows a rectangle with dimensions 20 cm by 10 cm from which a square with sides of length x cm is removed from each of the corners.
The shape in Figure 3 is then folded along the dotted lines to form a box, without a lid, in the shape of a cuboid, shown in Figure 4.
The volume of the box is $V\,\mathrm{cm}^3$ .

Find, to 3 significant figures, the value of x such that $\frac{dV}{dx}=0$ .

$\text{Solutions of } ax^2+bx+c=0 \text{ are } x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.$

$\frac{dV}{dx}=12x^{2}-120x+200$ $12x^{2}-120x+200=0$ $x=\frac{120\pm\sqrt{120^{2}-4\times12\times200}}{2\times12}$
Final answer:
x=2.11

Marking notes:
Allow $\frac{15-5\sqrt3}{3}$ . Do not accept 7.89.

All question bank results loaded

4.M Rates of change and stationary points question 1