Differentiation
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Question 330
The diagram shows the graph with equation y=f(x)y = f(x)y=f(x) where f(x)=(6x2+5x)e−xx∈Rf(x) = (6x^2 + 5x)e^{-x} \quad x \in \mathbb{R}f(x)=(6x2+5x)e−xx∈R
a.[3]
Show that f′(x)=e−x(7x+5−6x2)f'(x) = e^{-x}(7x + 5 - 6x^2)f′(x)=e−x(7x+5−6x2)
b.[3]
Hence, find, in simplest form, the exact coordinates of the stationary points of CCC
c.[3]
Find (i) the value of k k\,k where g(x)=kf(x)g(x) = kf(x)g(x)=kf(x) has range g(x)≥−4e1/2g(x) \geq -4e^{1/2}g(x)≥−4e1/2 and (ii) the value of m m\,m where h(x)=f(x)+m,x>0h(x) = f(x) + m, x > 0h(x)=f(x)+m,x>0 has range 3<h(x)≤25e−5/3+33 < h(x) \leq 25e^{-5/3} + 33<h(x)≤25e−5/3+3
Differentiation Questions
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.