Next question: Can you explain your previous answer about the connection between maxima and minima of a function f(x), and its first derivative f'(x)?
Answer A: The first derivative f'(x) is useless, and the maxima and minima of a function are useless too.
Answer B: The first derivative f'(x) tells me the slope of the tangent to f(x) at the point x. When f(x) passes a maximum or a minimum, the tangent is horizontal. This means the tangent has slope zero. This means f'(x) = 0