Question

Does an instantaneous rate of change of zero always indicate a local maximum or minimum? Explain

Answer 1

Explanation:

The derivative is the rate at which a function changes. Increasing function means positive derivative and decreasing function means negative derivative

Whenever the derivatives switch signs at a point, the derivative is zero at that point which makes it easier to locate the local maximum and minimum.

At the maximum, the function changes from increasing to decreasing, so the derivative changes from positive to negative, so the derivative is zero.

At the minimum, the function changes from decreasing to increasing, so the derivative changes from negative to positive, so the derivative is zero.