Question

find the critical number of a function f(x)=x^2​

Answer 1

Answer:

Here is your answer dear

Step-by-step explanation:

Definition

A number a in the domain of a given function f is called a critical number of f if f '(a) = 0 or f ' is undefined at x = a.

Example 1

Find the critical number(s) of the polynomial function f given by

f(x) = x 3 - 3x + 5

Solution to Example 1

The domain of f is the set of all real numbers. The first derivative f ' is given by

f '(x) = 3 x 2 - 3

f '(x) is defined for all real numbers. Let us now solve f '(x) = 0

3 x 2 - 3 = 0

x = 1 or x = -1

Since x = 1 and x = -1 are in the domain of f they are both critical numbers.

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