Asked by Mike
Let r(t) be a differentiable function that is positive and increasing. The rate of increase of r^3 is equal to 12 times the rate of increase of r when r(t)=?
Answers
Answered by
collins
the increasing rate or r^3 is 12 time of increasing rate of r
d/dt(r^3)=12dr/dt
3r^2dr/dt=12dr/dt
divde through by 3
r^2dr/dt=4dr/dt
r^2dr/dt-4dr/dt=0
dr/dt(r^2-4)=0
r^2-4=0
(r-2)(r+2)=0
r=2 or r=-2
that went awesome
now just have it in mind that any constant at all we always work
d/dt(r^3)=12dr/dt
3r^2dr/dt=12dr/dt
divde through by 3
r^2dr/dt=4dr/dt
r^2dr/dt-4dr/dt=0
dr/dt(r^2-4)=0
r^2-4=0
(r-2)(r+2)=0
r=2 or r=-2
that went awesome
now just have it in mind that any constant at all we always work
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