maxima..

[ish]

A Q on maxima and minima...

A rectangle in the fourth Quadrant of the xy plane has adjacent sides on the coordinate axes. if the vertex opposite (0,0) is on y=logx, what is the maxm area this rect can have?

The books says, Area A= x(-logx) as in the interval (0,1) the value of logx is negative.

But shouldnt the lengths be positive? and the area be x.logx ???

Someone help.

[piero]

The question says that (x, log x), the vertex opposite to (0,0), is in the 4th quadrant, so x>0 and log x <0, showing that 0<x<1. The lengths of the rectangle are x and - log x , so the area is - x ( log x ). Notice that because 0<x<1, both lengths and the area are positive. Drawing a figure might help.

[ish]

oops...that was silly of me wasnt it...thanks piero.