If a function has an absolute maximum at x = b , then f (b) is the largest value that f can attain. Similarly, if a function has an absolute minimum at x = b , then f (b) is the smallest value that f can attain. A function f has a local maximum at x = b if f (b) is the largest value that f attains “near b .” Similarly, a function f has a local minimum at x = b if f (b) is the smallest value that f attains “near b .” Taken together, the local maxima and local minima are known as the local extrema. A local minimum or local maximum may also be called a relative minumum or relative maximum.