Answer
$y=4x-4$
Work Step by Step
Use:
Theorem 5.2 :properties of ln(x),
Theorem 5.3.1:$\ \ \ (\displaystyle \ln x)^{\prime}=\frac{1}{x}$
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$y=f(x)=\ln x^{4}$=... property (3) of ln...$=4\ln x$
$f^{\prime}(x)=4\displaystyle \cdot\frac{1}{x}=\frac{4}{x}$
The slope of the tangent at (1,0) is $f^{\prime}(1)=\displaystyle \frac{4}{1}=4$
Point-slope equation of the tangent line:
$y-y_{0}=m(x-x_{0})$
$y-0=4(x-1)$
$y=4x-4$
For (b) and (c), see image attached.
