In Exercises $5-8,$ use the definition $f^{\prime}(a)=\lim _{x \rightarrow a} \frac{f(x)-f(a)}{x-a}$ to find the derivative of the given function at the indicated point. $$f(x)=\sqrt{x+1}, a=3$$
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Step 1: Recall the definition of the derivative at a point \(a\): \[f'(a) = \lim_{x \to a} \frac{f(x) - f(a)}{x - a}\] Show more…
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In Exercises $5-8,$ use the definition $f^{\prime}(a)=\lim _{x \rightarrow a} \frac{f(x)-f(a)}{x-a}$ to find the derivative of the given function at the indicated point. $$f(x)=2 x+3, a=-1$$
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