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Differentiation

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Question 369

The diagram shows the graph with equation y=f(x)y = f(x)y=f(x) where f(x)=(3x2+8x)e−xx∈Rf(x) = (3x^2 + 8x)e^{-x} \quad x \in \mathbb{R}f(x)=(3x2+8x)e−xx∈R

A smooth curve on arrowed x- and y-axes crosses the horizontal axis to the left of the vertical axis and at the origin, with a trough on the negative-x side and a smaller peak on the positive-x side.

a.

Find, in simplest form, the exact coordinates of the stationary points of CCC

[6]
b.

Find (i) the range of g g\,g where g(x)=2f(x)g(x) = 2f(x)g(x)=2f(x) and (ii) the range of h h\,h where h(x)=f(x)+2,x>0h(x) = f(x) + 2, x > 0h(x)=f(x)+2,x>0

[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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