Determining Maximum and Minimum
Example:
George had a function of stresses on a particular airplane part with respect to time in flight. He wished to determine the time when the part was under the most stress.
Given the function
f(t) = -t2 + 2 t + 3
George took the derivative of the function
f'(t) = -2t + 2
then determined that the derivative was equal to zero at t = 1.
The time of most stress was 1 minute into the flight.

One of the convenient uses for the derivative of a function is finding the maximum or minimum points of the function. The example on the definition page of this station shows that the derivative indicates the rate of change of a function. Put another way, the derivative measures the slope of the function at a particular point.

When the slope changes from positive to negative, the function is at its maximum when the slope is zero. When the slope changes from negative to positive, it is at its minimum when the slope is zero.