An automated solar tracker follows a path defined by the function
H(ϕ)=ϕ4+12ϕ2+24cosϕ H(\phi) = \phi^4 + 12\phi^2 + 24\cos \phi H(ϕ)=ϕ4+12ϕ2+24cosϕfor −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.
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.
