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+sinx+5 h(x) = \frac{1}{12}x^4 + \sin x + 5 h(x)=121x4+sinx+5for −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.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 327 questions covering 12.1 Gradients of Curves, 12.2 Differentiation from first principles, 12.3 Differentiating x^n, 12.4 Differentiating Quadratics, 12.5 Differentiating functions with two or more terms, 12.6 Gradients, Tangents and Normals, 12.7 Increasing and Decreasing Functions, 12.8 Second Order Derivatives, 12.9 Stationary Points, 12.10 Sketching Gradient Functions, and 12.11 Modelling with Differentiation, 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.
