(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=−1Find 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.
Hence find the set of values of x x\,x for which f(x)f(x)f(x) is increasing.
The curve with equation y=g(x)y = g(x)y=g(x) where
g(x)=sin5xx,0<x<π5 g(x) = \frac{\sin 5x}{\sqrt{x}}, \quad 0 < x < \frac{\pi}{5} g(x)=xsin5x,0<x<5πhas a stationary point at MMM.
Show that the xxx-coordinate of M M\,M satisfies the equation tan5x+kx=0\tan 5x + kx = 0tan5x+kx=0, where k k\,k is a constant to be found.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions 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, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
