Linear approximation practice

Name:
Group members:

Section:

Find the linear approximation to the function \[ f( t ) = t^{2} \left(t - 5\right) \] around $t= 7$.
$L_{ 7 }( t ) =$
Let $h(x) = - 7.3 \left(0.9 x^{2} - 0.1 x - 7.3\right)^{5}$. Determine a linear approximation $L(x)$ for $h(x)$ that is valid near $x=-0.4$. (In all answers, if you round numbers, keep at least four digits.)
$L(x) = $

Using the above linear approximation, estimate the value of $h(-0.43)$:

What is the actual value of $h(-0.43)$? $h(-0.43) = $
Let $f(x)$ be a differentiable function. Given just the information that $f(9.3) = 2.2$ and $\diff{ f }{x} \big|_{ x = 9.3 } = -8.5$, determine the equation of the tangent line at $x=9.3$.
$y = $

Using the above tangent line equation, estimate the value of $f(9.25)$: