The graph of consists of three straight-line segments that join the points , ,
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
The graph of y=f′(x) consists of three straight-line segments that join the points (−5,−1), (−2,2), (1,0), and (4,−3) in the xy-plane.
The x-axis is the horizontal reference line; the vertical scale is one unit per grid mark. No other critical points or discontinuities of f′ occur on the interval −5≤x≤4.
Answer the following, using only the information provided by the described graph of f′(x).
(a) Determine the intervals on which the original function f is increasing and the intervals on which it is decreasing. Clearly state your reasoning.
(b) Identify each x-value in the interval −5≤x≤4 at which f attains a relative maximum or a relative minimum. Classify each point and explain your justification.
(c) Describe the overall qualitative shape of a possible graph of y=f(x) on −5≤x≤4. Your description should include the location of turning points and the general behavior (increasing or decreasing) in each sub-interval.