calculus Question

Question

The power delivered by a battery to an apparatus of resistance R (in ohms) is
P =
2.4R
(R + 0.5)2
watts.
Find the rate of change of power with respect to resistance for
R = 9

Answer 1

P = 2.4R/(R+0.5)²

 

dP/dR = [(R+0.5)²(2.4) - 2.4R(2)(R+0.5)]/(R+0.5)⁴ 

 

Divide the numerator and denominator by R+0.5 to get:

 

dP/dR = [2.4(R+0.5) - 4.8R]/(R+0.5)³

 

         = (1.2 - 2.4R)/(R+0.5)³

 

So, when P = 9, dP/dR = -20.4/857.375 = -0.02379