Intervals of Increase?

Question

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

Answer 1

Take the derivative to find the condition dP/dR > 0.

 

 

dP/dR = -240/(0.4 + R)³

 

 

For R < -0.4, dP/dR > 0.   For R > -0.4, dP/dR < 0.

 

 

So the power increases for R in the interval, (-∞, -0.4).

 

 

Another way to find the answer is to graph P vs. R.  There is a vertical asymptote at R = -0.4, which divides the graph into two regions.  The region to the left is increasing; the region to the right decreasing.

 

 

But if resistance can only be positive (R ≥ 0), then there is no values of R that will increase the power.