Edexcel IGCSE Math A Higher 3.4 Hc Gradients Rates of Change Stationary Points Turning Questions

Practise using derivatives to find curve gradients, tangent equations, stationary points and maximum or minimum values.

Exam points

set dy/dx to a stated gradient and substitute each x-value into the curve
solve dy/dx=0 and calculate the coordinates of every stationary point
differentiate a contextual expression and verify the stationary value gives the required optimum

[Maximum number: 4]

The curve C has equation $y=5 x^{3}-x^{2}-6 x+4$

Find the x coordinate of each of these two points.

Show clear algebraic working.

Set the gradient equal to 2:
$15x^{2}-2x-6=2$ $15x^{2}-2x-8=0$

Factorise:
(3x+2)(5x-4)=0

Final answers:
$x=-\frac23,\qquad x=\frac45$

Allow -0.66 or better for $-\frac23$ .

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Edexcel IGCSE Math A Higher 3.4 Hc Gradients Rates of Change Stationary Points Turning Questions question 1