Question

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.

Answer 1

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

Answer 2

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)