advanced functions
posted by Anonymous on .
A generator produces electrical power, P, in watts, according to the function P(R)=(120R)/(0.4+R)^2,
where R is the resistance, in ohms. Determine the intervals on which the power is increasing.

I would take the first derivative, and make it >0 and solve for the intervals.

1. P&prime&prime(R)=0
>gives you the points at which the slope of P(R) changes from increasing to decreasing or vice versa.
2. Plug in a number between the intervals back into P&prime&prime(R)
> for example if you found:
R= 1 and R = 4
plug in 0 or 1 or 2 or 3 into P&prime&prime if its positive then the slopes are increasing on the interval from (1, 4)