2. (a) Demonstrate how we can use the definition of the derivative (second form) to find the derivative $f'(x)$ of the function $\frac{4}{\sqrt{x}}$ $f(x) = $ and then use the Power Rule to check if your formula of $f'(x)$ is correct. (b) Obtain an equation of the tangent line to the graph of $f(x)$ at $x = 4$. Sketch the graph of $f(x)$ together with this tangent line.
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Step 1: Using the definition of the derivative (second form), we have: f'(x) = lim(h->0) [f(x + h) - f(x)] / h f'(x) = lim(h->0) [(4 / sqrt(x + h)) - (4 / sqrt(x))] / h Show more…
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