Max Area Rectangle on y=cosx Curve

[ryan.1015]

Homework Statement

find, correct to five decimal places, the dimensions of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis and lying on the curve y=cosx

Homework Equations

The Attempt at a Solution

 

[LogicalTime]

this is a standard calc min/max problem. First make an equation of what you want to maximize
A=bh
the base is 2 times your x coordinate, and your height is just y so:
A= 2xy
now substute in your restraint equation y = cos(x)
A=2xcos(x)
now take the derivative with respect to x and set equal to zero. The solution should be the correct x value

 

[LogicalTime]

I'm getting a transcendental equation out of this cot(x)=x, guess you have to solve with your calculator from there unless I am making some mistake somewhere, usually these types of problems are a little cleaner to solve.

 

[Mark44]

I'm getting a transcendental equation out of this cot(x)=x, guess you have to solve with your calculator from there unless I am making some mistake somewhere, usually these types of problems are a little cleaner to solve.

That's what I get, so I think you're on the right track. A trial solution is x = pi/4, for which cot(pi/4) = 1. Those values aren't too far apart. I would keep trying different values, looking for values for which x and cot(x) are closer together, stopping when I get them to agree in 5 decimal places.