Linear approximation practice

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Find the linear approximation to the function \[ u( x ) = x^{2} \left(x - 4\right) \] around $x= 6$.
$L_{ 6 }( x ) =$
Let $h(x) = 1.3 \ln{\left (3.1 x^{2} - 6.2 x + 11.8 \right )}$. Determine the equation of the tangent line at $x=-0.3$. (In all answers, if you round numbers, keep at least four digits.)
$y = $

Using the above tangent line equation, estimate the value of $h(-0.27)$:

What is the actual value of $h(-0.27)$? $h(-0.27) = $
Let $g(x)$ be a differentiable function. Given just the information that $g(1.7) = 5.1$ and $g'(1.7) = -6.2$, determine the equation of the tangent line at $x=1.7$.
$y = $

Using the above tangent line equation, estimate the value of $g(1.7)$: