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.
717 exam-style questions on Edexcel A Level Maths Differentiation, 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. Each one has a worked solution and a mark scheme showing where the marks go.