question 4 of 10. step 1 of 2 consider the function: f(x)=x² - 6x + 8 step 1 of 2: find the critical values…

question 4 of 10. step 1 of 2 consider the function: f(x)=x² - 6x + 8 step 1 of 2: find the critical values of the function. separate multiple answers with commas. answer how to enter your answer (opens in new window) selecting a radio button will replace the entered answer value(s) with the radio button value. if the radio button is not selected, the entered answer is used. x = none

question 4 of 10. step 1 of 2 consider the function: f(x)=x² - 6x + 8 step 1 of 2: find the critical values of the function. separate multiple answers with commas. answer how to enter your answer (opens in new window) selecting a radio button will replace the entered answer value(s) with the radio button value. if the radio button is not selected, the entered answer is used. x = none

Answer

Explanation:

Step1: Find the derivative

The derivative of $f(x)=x^{2}-6x + 8$ using the power - rule $\frac{d}{dx}(x^{n})=nx^{n - 1}$ is $f'(x)=2x-6$.

Step2: Set the derivative equal to zero

Set $f'(x)=0$, so $2x - 6=0$. Solve for $x$: Add 6 to both sides: $2x=6$. Divide both sides by 2: $x = 3$.

Answer:

$x = 3$