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Those friendly functions that don't contain breaks, bends or cusps are "differentiable". Take their derivative, or just infer some facts about them from the Mean Value Theorem.

Local Linear Approximation

If \(f(1)=4\) and \(f'(1)=6,\) which of the following is the best local linear approximation for \(f(1.01)?\)

Estimate the value of \(\sqrt[3]{0.979}\) using local linear approximation for the function \(f(x)=\sqrt[3]{1+x}.\)

Use differentiation to estimate the value of \(\sqrt{16.5}\).

Estimate the value of \(\displaystyle \frac{6}{(1-x)^2}\) at \(x=0.02\) using local linear approximation.

What is the local linear approximation of the function \(f(x)=14x^3-5x\) near \(x = 1?\)


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