The body mass index [BMI] for an adult human is given by the function B = w/h^2

Question

The body mass index [BMI] for an adult human is given by the function B = w/h^2 where w is the weight measured in kilograms and h is the height measured in meters. [The BMI for units of pounds and inches is B = 703 w/h^2.) Find the rate of change of the BMI with respect to weight at a constant height. For fixed h, is the BMI an increasing or decreasing function of w? Find the rate of change of the BMI with respect to height at a constant weight. For fixed w, is the BMI an increasing or decreasing function of h?

Explanation / Answer

given BMI is

B = w / h^2

( a )

differentaite B wih respect to w ,where h is constant

so

d/dw(B) = d/dw( w / h^2 )

= 1 / h^2 ( d/ dw (w)

dB / dw = 1 / h^2

therefore rate of change of B with respect to weight is 1 / h^2

( b ) for given function B = w / h^2

differentaite B wih respect to h ,where w is constant

rate of change of B with respect to weight is constant ,based on w is neither decreasing nor increasing ,for fixed h

( c ) for given function B = w / h^2

d/dw(B) = d/dw( w / h^2 )

= w ( d/ dw (h^-2)

dB / dw = -2w / h^3

therefore rate of change of B with respect to weight is -2w / h^3

( d )

for fixed w

rate of change of B with respect to weight is constant ,based on h is decreasing function of h

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