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Differentiation

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Question 489

(i) The function f f\,f is defined by

f(x)=(2x−5)2x+1,x≠−1 f(x) = \frac{(2x - 5)^2}{x + 1}, \quad x \neq -1 f(x)=x+1(2x−5)2​,x=−1
a.

Find f′(x)f'(x)f′(x) in the form P(x)Q(x)\displaystyle \frac{P(x)}{Q(x)}Q(x)P(x)​ where P(x)P(x)P(x) and Q(x)Q(x)Q(x) are fully factorised quadratic expressions.

[4]
b.

Hence find the set of values of x x\,x for which f(x)f(x)f(x) is increasing.

[2]
c.

The curve with equation y=g(x)y = g(x)y=g(x) where

g(x)=sin⁡5xx,0<x<π5 g(x) = \frac{\sin 5x}{\sqrt{x}}, \quad 0 < x < \frac{\pi}{5} g(x)=x​sin5x​,0<x<5π​

has a stationary point at MMM.

Show that the xxx-coordinate of M M\,M satisfies the equation tan⁡5x+kx=0\tan 5x + kx = 0tan5x+kx=0, where k k\,k is a constant to be found.

[3]
Markscheme

Differentiation Questions

  1. A Level
  2. /Maths
  3. /Differentiation

717 exam-style questions on Edexcel A Level Maths Differentiation, covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change. Each one has a worked solution and a mark scheme showing where the marks go.

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