Linear approximation practice

Name:
Group members:

Section:

Let $g(x) = \left(8 x^{2} - 2.5 x - 8.8\right) \ln{\left (x \right )}$. Determine a linear approximation $L(x)$ for $g(x)$ that is valid near $x=0.7$. (In all answers, if you round numbers, keep at least four digits.)
$L(x) = $

Using the above linear approximation, estimate the value of $g(0.65)$:

What is the actual value of $g(0.65)$? $g(0.65) = $
Let $f(x)$ be a differentiable function. Given just the information that $f(6.1) = 0.6$ and $\diff{ f }{x} \big|_{ x = 6.1 } = -3.8$, determine the equation of the tangent line at $x=6.1$.
$y = $

Using the above tangent line equation, estimate the value of $f(6.09)$:
Find the linear approximation to the function \[ r( x ) = e^{- x + 1} \left(x - 4\right) \] around $x= 1$.
$L( x ) =$