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3.6 Differentiation (A-level only)

3.6 Differentiation (A-level only)

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Question 265

(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

3.6 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Differentiation (A-level only)

333 exam-style questions on WJEC A Level Maths 3.6 Differentiation (A-level only), covering 3.6.1 Differentiation (A-level only), 3.6.2 Differentiation (A-level only), 3.6.3 Differentiation (A-level only), 3.6.4 Differentiation (A-level only), 3.6.5 Differentiation (A-level only), 3.6.6 Differentiation (A-level only), 3.6.7 Differentiation (A-level only), and 3.6 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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