Question

(a) the derivative of a function f at x, denoted by f(x), is f(x) = limₕ→₀ f(x + h) - f(x) / h provided that the limit exists. use the definition of the derivative of f at x to find the derivative of the given function f(x) when x = 4.
f(4) = limₕ→₀ □ - 1/x / h

Explanation:

Step1: Substitute \(x = 4\) into \(f(x)\)

We know that \(f(x)=\frac{1}{x}\). So \(f(4 + h)=\frac{1}{4 + h}\) and \(f(4)=\frac{1}{4}\).

Step2: Substitute into the derivative formula

$$
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Answer:

\(\lim_{h
ightarrow0}\frac{\frac{1}{4 + h}-\frac{1}{4}}{h}\)