Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - Chapter Review Exercises - Page 162: 17


$ f(4)=-2$, $ f'(4)=3$

Work Step by Step

The equation of the tangent line is $ y=f(a)+f'(a)(x-a)$ This implies that $ f(4)+f'(4)(x-4)=3x-14$ From the above equation, we have $ f'(4)\times x=3x $ and $[f(4)-4\times f'(4)]=-14$ Thus, we obtain $ f'(4)=3$ and $ f(4)=-14+(4\times3)=-2$
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