# Homework Help: Finding largest area

1. Nov 23, 2008

### ryan.1015

1. The problem statement, all variables and given/known data
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

2. Relevant equations

3. The attempt at a solution

2. Nov 23, 2008

### 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

3. Nov 23, 2008

### 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.

4. Nov 23, 2008

### Staff: Mentor

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.