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quackensack

Member

Registered: 2007-02-27

Posts: 47

partial derivatives problem

Not really sure how this is done so any help would be appreciated.

The function S(w, h) = (15.63w^0.425) * (h^.0725) gives the approximate surface area (in sq. inches) of a person h inches tall who weighs w pounds.

1) A boy grows taller while maintaining a weight of 130 pounds. At what rate is his surface area increasing when he's 5'4" tall?

2) Now at his full height of 5'9", he goes to the gym and bulks up. At what rate is his body surface increasing when he reaches 140 pounds?

gnitsuk

Member

Registered: 2006-02-09

Posts: 121

Re: partial derivatives problem

1) Here w is constant and so S is really only a function of h. We can differemtiate this w.r.t. h to get the rate of change of the boys surface area with height at constant weight:

So when w = 130 pounds and h = 5'4"  = 64 inches, we have:

2) Here h is constant and so S is a function only of w. We can differentiate w.r.t. w to get the rate of change of surface area with weight at constant height:

So when w = 140 pounds and h = 69 inches we have:

Last edited by gnitsuk (2007-03-15 22:05:03)