Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.1 Exercises - Page 326: 67

Answer

$y=5x-2$

Work Step by Step

Theorem 5.2 :properties of ln(x), Theorem 5.3.1:$\ \ \ (\displaystyle \ln x)^{\prime}=\frac{1}{x}$ -------------------- $y=f(x)=3x^{2}-\ln x$ $f^{\prime}(x)=6x-\displaystyle \frac{1}{x}$ The slope of the tangent at ($1,3$) is $f^{\prime}(1)=6-1=5$ Point-slope equation of the tangent line: $y-y_{0}=m(x-x_{0})$ $y-3=5(x-1)$ $y=5x-5+3$ $y=5x-2$ For (b) and (c), see image attached.
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