The graph of a differentiable function is drawn on a square grid
MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
The graph of a differentiable function h is drawn on a square grid. Along the x-axis, each horizontal square represents 2 units; along the y-axis, each vertical square represents 5 units.
Exact coordinates of several visible points are provided.
x -value −6 −2 1 4 7
h(x) −5 10 12 4 −1
The curve is smooth except for a sharp corner at x=1, and no other local maxima or minima occur on the closed interval [−6,7].
(a) Using the stated scale factors, write the exact coordinates of the point where h attains a local maximum.
(b) List all x-values in [−6,7] at which h′(x)=0 or h′(x) does not exist. For each of these critical points, classify it as a local maximum, local minimum, or neither, and justify your classification based on features of the graph.
(c) Determine the absolute maximum value and the absolute minimum value of h on [−6,7]. Explain how the non-standard scale influences your reasoning.