A curve represents the thermal expansion of a composite alloy, where the length LLL is defined as a function of the temperature θ\thetaθ such that L=f(θ)L = f(\theta)L=f(θ). It is observed that the graph has a point of inflection at θ=185\theta = 185θ=185. Given that f′(185)=αf'(185) = \alphaf′(185)=α and f′′(185)=βf''(185) = \betaf′′(185)=β, where α\alphaα and β\betaβ are constants, identify which of the following statements must be true:
f′(185)=0 f'(185) = 0 f′(185)=0 f′′(185)=0 f''(185) = 0 f′′(185)=0 f′(185)≠0 f'(185) \neq 0 f′(185)=0 f′′(185)<0 f''(185) < 0 f′′(185)<0Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions 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, 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.
