Linear approximation practice

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Let $f(x)$ be a differentiable function. Given just the information that $f(-3.5) = -4.9$ and $\diff{ f }{x} \big|_{ x = -3.5 } = 1.5$, determine the equation of the tangent line at $x=-3.5$.
$y = $

Using the above tangent line equation, estimate the value of $f(-3.55)$:
Let $f(x) = \left(0.3 x^{2} + 2.2 x + 5.8\right) \ln{\left (x \right )}$. Determine a linear approximation $L(x)$ for $f(x)$ that is valid near $x=4.6$. (In all answers, if you round numbers, keep at least four digits.)
$L(x) = $

Using the above linear approximation, estimate the value of $f(4.63)$:

What is the actual value of $f(4.63)$? $f(4.63) = $
Find the linear approximation to the function \[ q( y ) = \left(y - 7\right)^{3} - 9 \] around $y= 8$.
$L_{ 8 }( y ) =$