Linear approximation practice

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Let $g(x) = 3.1 \ln{\left (6 x^{2} + 120 x + 603.6 \right )}$. Determine the equation of the tangent line at $x=-1.4$. (In all answers, if you round numbers, keep at least four digits.)
$y = $

Using the above tangent line equation, estimate the value of $g(-1.38)$:

What is the actual value of $g(-1.38)$? $g(-1.38) = $
Let $g(x)$ be a differentiable function. Given just the information that $g(-7.5) = 5.8$ and $g'(-7.5) = 3.4$, determine the equation of the tangent line at $x=-7.5$.
$y = $

Using the above tangent line equation, estimate the value of $g(-7.49)$:
Find the linear approximation to the function \[ v( y ) = y^{2} \left(y - 5\right) \] around $y= 6$.
$L_{ 6 }( y ) =$