Derivative Geometry Help (1 Viewer)

alussovsky

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The question:

7. The sum of the radii of two circles is constant, so that r1 + r2 = k, where k is constant
(a) Find an expression for the sum of the areas of the circles in terms of one variable only
(b) Hence show that the sum of the areas is least when the circles are congruent

Thank you for your help!
 

fan96

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and



noting that is a constant, we can then eliminate by doing one substitution.
 

alussovsky

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and



noting that is a constant, we can then eliminate by doing one substitution.
Oh, I get that part now! Aaaahh, sorry, I think I was a bit out of it before, lol

But uhh, how would you do part b?
 

fan96

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Oh, I get that part now! Aaaahh, sorry, I think I was a bit out of it before, lol

But uhh, how would you do part b?
Part b) is a standard maximisation question.

will be a quadratic function of .

By inspecting the coefficient of we can see this is a concave-up ("smiley face") parabola and hence has a global minimum, though we will need to determine if this global minimum lies in the domain .

Because the maximum lies on a turning point, we may consider the derivative and solve



You will eventually arrive at .
 

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