There is a lighthouse that is 4 miles from the closest point, B, on a straight beach. 4 miles east of B, is point C. If the keeper of the lighthouse can row his boat at 3 mi/h and walk at 5 mi/h (On a treadmill, I speedwalk at approximately 4.6 mi/h, so this guy must be pretty fit!). Find the distance between B and C he should land to minimize time taken.

For this, I let x be the distance between B and D, the point where he would land his boat.

The distance traveled across water would then be $\displaystyle \sqrt{x^2+16}$

Wouldn't the equation be $\displaystyle f(x)=3\sqrt{x^2+16}+5(4-x)=3\sqrt{x^2+16}-5x+20$

thus,

$\displaystyle f`(x)=\frac{3x}{\sqrt{x^2+16}}-5\\f`(x)=0;\5\sqrt{x^2+16}=3x\\25(x^2+16)=9x^2\\x= \sqrt{-25}???$

So, I was wondering if this was just a faulty problem, if I messed up, or what. I feel like I overlooked something ridiculous.