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Differentiation

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Question 537

An automated solar tracker follows a path defined by the function

H(ϕ)=ϕ4+12ϕ2+24cos⁡ϕ H(\phi) = \phi^4 + 12\phi^2 + 24\cos \phi H(ϕ)=ϕ4+12ϕ2+24cosϕ

for −π≤ϕ≤π-\pi \le \phi \le \pi−π≤ϕ≤π, where HHH is the vertical displacement in decimeters and ϕ\phiϕ is the angle of rotation in radians. Determine whether the curve with equation y=H(ϕ)y = H(\phi)y=H(ϕ) has a point of inflection at the point where ϕ=0\phi = 0ϕ=0. Fully justify your answer.

[5]
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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