- #1

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- 0

A. (3, 0)

B. (3 1/4, 0)

C. (3 3/4, 0)

D. (4 1/2, 0)

E. (5, 0)

What I did:

f(x) = AP + PB =\(\displaystyle \sqrt{5^2+x^2}+(10-x)=\sqrt{25+x^2}+10-x\)

In order to make AP + PB minimum, so:

f'(x) = 0

\(\displaystyle \frac12(25+x^2)^{-\frac12}(2x)+(-1)=0\)

\(\displaystyle \frac{x}{\sqrt{25+x^2}}=1\)

\(\displaystyle x=\sqrt{25+x^2}\)

\(\displaystyle x^2=25+x^2\)

This is where I got stuck. Subtracting \(\displaystyle x^2\) from both sides would leave me with 0 = 25 which is obviously incorrect. Where did I do wrong?