## marigirl one year ago Differentiate with respect respect to w 4r^2=l^2+w^2

1. marigirl

I understand the right side will be $= 2l \frac{ dl }{ dw }+2w$ the left side shown to be zero in my model answers.. plz help

2. marigirl

@IrishBoy123

3. anonymous

is it given that L is a function of w, is r a constant?

4. marigirl

im trying to figure out the maximum area of a rectangle inside a circle. so the above equation was used to express the radius

5. marigirl

6. marigirl

now that i think of it, yes r is a constant i guess becuase i am after the maximum l and w in order to get the maximum area...

7. anonymous

yes radius is a constant in this problem, length and width are variables . that is why you have 0 when you take derivative of r^2

8. phi

***im trying to figure out the maximum area of a rectangle inside a circle*** if you allowed "r" to vary, then you are changing the circle (i.e. its size) and the problem makes no sense: what is the biggest rectangle I can put in a circle, if I am allowed to change the size of the circle? It makes more sense to ask the question: what is the biggest rectangle I can put in a circle that has a *fixed radius* r? in other words, we should treat r as a constant in this problem.

9. marigirl

Thank you!