Differentiate with respect respect to w

4r^2=l^2+w^2

Question

Differentiate with respect respect to w

4r^2=l^2+w^2

marigirl · Answer

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

marigirl · Answer

@IrishBoy123

anonymous · Answer

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

marigirl · Answer

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

marigirl · Answer

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marigirl · Answer

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...

anonymous · Answer

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

phi · Answer

***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.

marigirl · Answer

Thank you!