A problem in minima and maxima applicatios ( )please

[faisal-tesla]

a problem in minima and maxima applicatios (urgent !)please

Homework Statement

A straight river 3km wide runs due east. A cable is to be laid from a point A on the south bank of the river to a point B on its north bank, 9km downstream from A. The cable is to be laid in a straight line from A to some point C on the north bank, and from there it is to be laid in a straight line along the north bank to B. If cable laid through water costs $M per kilometre and cable laid along the bank costs $N per kilometre with M > N, where should C be located to minimise the total cost of the cable? What is the minimum cost? Prove that your answer corresponds to the minimum cost

Homework Equations

The Attempt at a Solution

I got a number in terms of N and M. I also have to check the end point (x=0, x=9)

However, I couldn't prove the value is a minimum because it basically depends on N/M


regards,
Faisal

 

[jbunniii]

If the function is differentiable and you have exactly one point x in [0,9] where the derivative is zero, then the only candidates for the locations of the minimum and maximum are x, 0, and 9. So just check the function value at those three points: whichever one is smallest is the minimum.