Question
Find the slope and an equation of the tangent line to the graph of the function $f$ at the specified point.$$f(x)=\sqrt{x}+\frac{1}{\sqrt{x}} ;\left(4, \frac{5}{2}\right)$$
Step 1
Substitute \(x = 4\) into the function: \[ f(4) = \sqrt{4} + \frac{1}{\sqrt{4}} = 2 + \frac{1}{2} = \frac{5}{2}. \] Since \(f(4) = \frac{5}{2}\), the point \((4, \frac{5}{2})\) is indeed on the graph. Show more…
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