Linear approximation practice

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Let $g(x)$ be a differentiable function. Given just the information that $g(8.4) = 6.5$ and $g'(8.4) = -5.9$, determine the equation of the tangent line at $x=8.4$.
$y = $

Using the above tangent line equation, estimate the value of $g(8.42)$:
Let $g(x) = 1.7 \left(0.4 x^{2} + 2.4 x + 6.6\right)^{3}$. Determine a linear approximation $L(x)$ for $g(x)$ that is valid near $x=-1.2$. (In all answers, if you round numbers, keep at least four digits.)
$L(x) = $

Using the above linear approximation, estimate the value of $g(-1.16)$:

What is the actual value of $g(-1.16)$? $g(-1.16) = $
Find the linear approximation to the function \[ v( x ) = \left(x - 6\right)^{3} - 2 \] around $x= 8$.
$L_{ 8 }( x ) =$