Edexcel IGCSE Math A 3.4.HC Gradients, Rates & Stationary Points

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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3.4.HC Gradients, rates of change, stationary points, turning question 1