Linear approximation practice

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Let $f(x)$ be a differentiable function. Given just the information that $f(0.7) = 3.6$ and $\diff{ f }{x} \big|_{ x = 0.7 } = 7.1$, determine a linear approximation $L(x)$ for $f(x)$ that is valid near $x=0.7$.
$L(x) = $

Using the above linear approximation, estimate the value of $f(0.74)$:
Let $f(x) = - 3 \left(1.6 x^{2} + 2.9 x - 9.9\right)^{5}$. Determine the equation of the tangent line at $x=1$. (In all answers, if you round numbers, keep at least four digits.)
$y = $

Using the above tangent line equation, estimate the value of $f(0.96)$:

What is the actual value of $f(0.96)$? $f(0.96) = $
Find the linear approximation to the function \[ w( z ) = z^{2} \left(z - 4\right) \] around $z= 6$.
$L_{ 6 }( z ) =$