# Application of calculus?

• June 29th 2008, 07:04 AM
fardeen_gen
Application of calculus?
Power supplied by a cell to a resistance R is given by P = [E/(R + r)]^2 * R. E and r, remain constant. For what value of R, maximum power is supplied to resistance R?

Ans: R=r
Can anyone explain the method?
• June 29th 2008, 07:10 AM
galactus
If you differentiate, you get:

$\frac{E^{2}(r-R)}{(R+r)^{3}}$

Setting to 0 and solving we see that:

$(r-R)=0, \;\ \therefore{R=r}$