Edexcel A-Level Mathematics AS P2.7.1 Applications of Differentiation Questions

Practise Edexcel IAL Mathematics P2.7.1 by differentiating functions, solving for stationary points, justifying maxima or minima and finding increasing or decreasing intervals.

Exam points

Differentiate functions and set dy/dx = 0 to find stationary points or model values.
Use d²y/dx² or derivative sign changes to justify maxima and minima.
Solve f'(x) > 0 or f'(x) < 0 to give intervals of increase or decrease.

[Maximum number: 3]

In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.

f(x)=4 x^{3}+13 x^{2}-10 x+8

Find the range of values of x for which f(x) is decreasing.

$f'(x)=12x^2+26x-10$ $12x^2+26x-10=0$ $2(6x^2+13x-5)=0$ (2x+5)(3x-1)=0 $x=-\frac52,\ \frac13$ $f(x)\text{ is decreasing for }-\frac52<x<\frac13$

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Edexcel A-Level Mathematics AS P2.7.1 Applications of Differentiation Questions question 1