Linear approximation practice

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Find the linear approximation to the function $u( x ) = x^{3} - x$ around $x= 3$ .
$L( x ) =$
Let $h(x) = - 6.7 e^{1.5 x^{2} + 3.5 x + 1}$ . Determine the equation of the tangent line at $x=2$ . (In all answers, if you round numbers, keep at least four digits.)
$y =$

Using the above tangent line equation, estimate the value of $h(1.98)$ :

What is the actual value of $h(1.98)$ ? $h(1.98) =$
Let $h(x)$ be a differentiable function. Given just the information that $h(4.5) = 8.1$ and $\diff{ h }{x} \big|_{ x = 4.5 } = -7.7$ , determine the equation of the tangent line at $x=4.5$ .
$y =$

Using the above tangent line equation, estimate the value of $h(4.51)$ :