Linear approximation practice

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Let $f(x)$ be a differentiable function. Given just the information that $f(5.1) = 0.5$ and $f'(5.1) = 0$, determine the equation of the tangent line at $x=5.1$.
$y = $

Using the above tangent line equation, estimate the value of $f(5.05)$:
Let $g(x) = 3.1 e^{- 2 x^{2} - 3.1 x + 1}$. Determine the equation of the tangent line at $x=-0.1$. (In all answers, if you round numbers, keep at least four digits.)
$y = $

Using the above tangent line equation, estimate the value of $g(-0.15)$:

What is the actual value of $g(-0.15)$? $g(-0.15) = $
Find the linear approximation to the function \[ g( t ) = t^{3} - t \] around $t= 2$.
$L_{ 2 }( t ) =$