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1.7 Differentiation

1.7 Differentiation

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Question 262

A landscape architect is designing a section of a path. The elevation h h\,h of the path (in meters) relative to a reference level is modeled by the function

h(x)=112x4+sin⁡x+5 h(x) = \frac{1}{12}x^4 + \sin x + 5 h(x)=121​x4+sinx+5

for −π≤x≤π-\pi \le x \le \pi−π≤x≤π, where x x\,x represents the horizontal distance in meters from a marker.

Determine whether the curve with equation y=h(x)y = h(x)y=h(x) has a point of inflection at the point where x=0x = 0x=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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