of xo. You may use without proof the following result, which is a consequence of the Mean-Value Theorem (discussed in Section 4.8). Theorem. Let f be continuous at xo and sup- pose that limf'(x) exists. Then f is differentiable at xo, and f'(xo) = limf(x). 67. Show that '+x+1, *SI * > I f(x) = 3x₂ is continuous at x = 1. Determine whether f is differen- tiable at x = 1. If so, find the value of the derivative there. Sketch the graph of f.

of xo. You may use without proof the following result, which is a consequence of the Mean-Value Theorem (discussed in Section 4.8). Theorem. Let f be continuous at xo and sup- pose that limf'(x) exists. Then f is differentiable at xo, and f'(xo) = limf(x). 67. Show that '+x+1, SI > I f(x) = 3x₂ is continuous at x = 1. Determine whether f is differen- tiable at x = 1. If so, find the value of the derivative there. Sketch the graph of f.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter6: Applications Of The Derivative

Section6.CR: Chapter 6 Review

Problem 1CR

See similar textbooks