Locating critical points a. Find the critical points of

Chapter 7, Problem 23E

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QUESTION:

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.

\(f(x)=3 x^{2}-4 x+2\)

Questions & Answers

QUESTION:

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.

\(f(x)=3 x^{2}-4 x+2\)

ANSWER:

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 1 1 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 f (x) = 4x 16x f (x) = 0 =4x 16x 4x ( x - 4) = 0 4x(x+2)(x-2) = 0

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