Given:
The power generated by an electrical circuit (in watts) as a function of its current x (in amperes) is modeled by
To find:
The current which will produce the maximum power.
Solution:
We have,
Differentiate with respect to x.
...(i)
To find the extreme point equate P'(x)=0.
Divide both sides by -30.
Differentiate (i) with respect to x.
(Maximum)
It means, the given function is maximum at x=4.
Therefore, the current of 4 amperes will produce the maximum power.
After clarification we see the respective diameters are
We're asked about the ratio
Now we can go through the choices.
A. If a = 4 and b = 6, then cell a is 100 times greater than cell b.
It would be more proper to say the diameter of cell A is 100 times the diameter of cell B, but yes, this is TRUE.
B. If a = 4 and b = 6, then cell b is 100 times greater than cell a.
FALSE. 10 to the minus 4 is 100 times bigger than 10 to the minus 6, so a is bigger.
C. If a = 4 and b = 6, then cell a is 2 times greater than cell b.
FALSE. We already calculated its 100 times bigger.
D. If a = 4 and b = 6, then cell b is 2 times greater than cell a.
FALSE.
