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1.7 Differentiation

1.7 Differentiation

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Question 226

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.

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Markscheme

1.7 Differentiation Questions

  1. A Level
  2. /Maths
  3. /1.7 Differentiation

425 exam-style questions on OCR A Level Maths 1.7 Differentiation, covering 1.7.1 Derivative as gradient of the tangent, 1.7.2 Gradient of the tangent at a point, 1.7.3 Sketching the gradient function, 1.7.4 Second derivatives, 1.7.5 Second derivative as rate of change of gradient, 1.7.6 Convex, concave and points of inflection (A-level only), 1.7.7 Differentiation from first principles for powers of x, 1.7.8 Differentiation from first principles for sin x and cos x (A-level only), 1.7.9 Differentiating x^n, 1.7.10 Differentiating e^(kx) and a^(kx) (A-level only), 1.7.11 Differentiating trigonometric functions (A-level only), 1.7.12 Derivative of ln x (A-level only), 1.7.13 Tangents and normals, 1.7.14 Stationary points, 1.7.15 Increasing and decreasing functions, 1.7.16 Points of inflection (A-level only), 1.7.17 Product and quotient rules (A-level only), 1.7.18 Chain rule (A-level only), 1.7.19 Parametric and implicit differentiation (A-level only), 1.7.20 Constructing differential equations (A-level only), and 1.7 Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.

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