F(r)=1.5r^4, where F represents the flow in cubic centimeters per second through a pipe of radius r. If r=1, how much will a small increase in radius change the flow (try it with delta(r)=0.1)? If r=2, how will a small increase in radius change the flow?

Question

F(r)=1.5r^4, where F represents the flow in cubic centimeters per second through a pipe of radius r. If r=1,  how much will a small increase in radius change the flow (try it with delta(r)=0.1)? If r=2, how will a small increase in radius change the flow?

anonymous · Answer

if r=1, Delta F(r) = 0.6
if r=2, Delta F(r)= 4.8

anonymous · Answer

Ok, so I get that much, but how is this related to derivatives? Isn't this just plugging 1, 1.1, 2, and 2.1 into the function f(r)?

anonymous · Answer

the very "change" = "increase",  we are trying to find here is the derivative. derivative of a function is the rate of change of function , increase or decrease at that point.

anonymous · Answer

Thanks. Would you mind explaining how you got 4.8?

anonymous · Answer

The relationship is :$$F=1.5r^{4}$$thus$$\frac{dF}{dr}=4\times 1.5r^{3}=6r^{3}$$so the rate of change at r = 1.0 is ;$$\frac{dF}{dr}(1)=6$$so an estimate of the flow increase is 6 x 0.1 = 0.6, you can do the same analysis for r = 2