Mathematics

Problem

Let

f(x)=\sqrt{x}

. A student wants to estimate

\sqrt{26}

using information at

x=25

. (a) Calculate

f'(x)

and write the equation of the line tangent to the graph of

f

x=25

. Express the equation in point–slope form. (b) Use the tangent line from part (a) to approximate

\sqrt{26}

. Show all work leading to your numerical result. (c) Determine whether the approximation obtained in part (b) is an underestimate or an overestimate of

\sqrt{26}

. Fully justify your answer using appropriate calculus reasoning.

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