Question

A charge Q is to be divided in two objects. What should be the values of the charges on the two objects so that the force between the objects can be maximum?
Explain why we differentiate to get the maximum value or solve this question in any other method.

Answer 1

y = f(x)
When we differentiate a function, it basically gives you the slope. Now at maximum or minimum, the value of slope is zero.
So, $\frac{dy}{dx}=0$ gives you position of maxima or minima.