Solved: 3132. One-sided derivatives The right-sided and
Chapter 3, Problem 32(choose chapter or problem)
3132. One-sided derivatives The right-sided and left-sided derivatives of a function at a point a are given by f+1a2 = lim hS0+ f 1a + h2 - f 1a2 h and f-1a2 = lim hS0- f 1a + h2 - f 1a2 h , respectively, provided these limits exist. The derivative f 1a2 exists if and only if f+1a2 = f-1a2. a. Sketch the following functions. b. Compute f+1a2 and f-1a2 at the given point a. c. Is f continuous at a? Is f differentiable at a? f 1x2 = b 4 - x2 if x 1 2x + 1 if x 7 1 ; a = 1
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