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 AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
