23–30. Locating critical points

a. Find the critical points of the following functions on the domain or on the given interval.

b. Use a graphing utility to determine whether each critical point corresponds to a local minimum, local maximum, or neither.

f(x) = 1/x - ln x

STEP_BY_STEP SOLUTION Step-1 Let f be a continuous function defined on an open interval containing a number ‘c’.The number ‘c’ is critical value ( or critical number ). If f (c) = 0 or f (c) is undefined. A critical point on that graph of f has the form (c,f(c)). Example ; Find all critical points of f(x) = x 8x .2 Because f (x) is a polynomial function, its domain is all real numbers. 1 3 f (x) = 4x 16x 1 f (x) = 0 =4x 16x