calculus problem

Question

A 0 degrees celsius, the heat loss H (in kilocalories per square meter per hour) from a person's body can be modeled by H=33(10sqrt v -v10.45, where v is the wind speed (in meters per second). 

 

a.) Find dH/dv and interpret its meaning in this situation

 

b.) Find the rates of change of H when v=2 ad when v=5

Answer 1

As written, your equation for H is ambiguous. I think it's:

 

     H = 33(10√(v) -10.45v) = 330v^1/2 - 344.85v

 

a)  Differentiate using the chain and power rules:

 

     dH/dv = 330·(1/2)(v)^-1/2 - 344.85

 

     dH/dv is the rate at which a person's body heat loss changes as the wind speed changes.

 

b)  Plug v = 2 then v = 5 into dH/dv and compute the answers