(a) State the rule that allows you to decide whether a stationary point of a…
MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
(a) State the rule that allows you to decide whether a stationary point of a twice–differentiable real function is a local maximum or a local minimum.
(a) (a) State the rule that allows you to decide whether a stationary point of a twice–differentiable real function is a local maximum or a local minimum.
(b) (b) A differentiable function g satisfies g′(2)=0 and g′(5)=0. Further, g′′(2)=−4 and g′′(5)=9.
(i) Explain what information the given second–derivative values provide about the curvature of the graph at x=2 and x=5.
(c) (ii) Hence identify the nature of the stationary points of g at x=2 and x=5.
(d) (iii) If g(2)=7 and g(5)=3, write the coordinates of both stationary points.