### Home > CALC > Chapter 5 > Lesson 5.1.3 > Problem 5-27

5-27.

Identify the maxima and minima of

Find CANDIDATES for maxima and minima by setting the first derivative equal to 0.

Decide if each candidate is a maximum, minimum or neither. You could check for slope change by evaluating the 1st-derivative at points close to each candidate. You could evaluate each candidate in the 2nd-derivative. If the graph is concave up, it cannot have a local max. And vice versa.

Recall that maxima and minima are *y*-values, not *x*-values. So use *f*(*x*) to find the *y*-value of each candidate.

(0, 40) is a local maximum, (4, 8) is a local minimum, (5, 8.75) is a local maximum, and (5, 8.75) is the global maximum. There is no global minimum.