A curve is defined by the equation y=g(x)y = g(x)y=g(x). It is known that the curve has a point of inflection at x=−4x = -4x=−4. Given that g′(−4)=kg'(-4) = kg′(−4)=k and g′′(−4)=mg''(-4) = mg′′(−4)=m, where kkk and mmm are constants, identify which of the following statements must be true:
g′(−4)=0 g'(-4) = 0 g′(−4)=0 g′′(−4)=0 g''(-4) = 0 g′′(−4)=0 g′(−4)≠0 g'(-4) \neq 0 g′(−4)=0 g′′(−4)>0 g''(-4) > 0 g′′(−4)>0375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.