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Differentiation

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Question 300

The diagram shows the graph with equation y=f(x)y = f(x)y=f(x) where f(x)=x2e−xx∈Rf(x) = x^2e^{-x} \quad x \in \mathbb{R}f(x)=x2e−xx∈R

An unnumbered x-y graph of y = x²e⁻ˣ, with a curve that touches the origin and stays above the x-axis.

a.

Show that f′(x)=e−x(2x−x2)f'(x) = e^{-x}(2x - x^2)f′(x)=e−x(2x−x2)

[3]
b.

Hence, find, in simplest form, the exact coordinates of the stationary points of CCC

[3]
c.

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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