MATHEMATICS · Multi-part · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives
Problem
A function g is defined for −5≤x≤3. The graph of g consists of two straight-line segments that join the points (−5,2) to (−2,−4) and (−2,−4) to (3,6). Grid lines on both axes are one unit apart.
Throughout this problem, g′(x) denotes the derivative of g at x, when it exists.
(a) Calculate the slope of the segment connecting (−5,2) and (−2,−4). State this value as g′(x) for all x in the open interval (−5,−2).
(b) Calculate the slope of the segment connecting (−2,−4) and (3,6). State this value as g′(x) for all x in the open interval (−2,3).
(c) Determine whether g′(−2) exists. Justify your answer by comparing appropriate one-sided limits of the difference quotient.