on what interval is f(x)=x² - 6x + 14 decreasing? enter inf for infinity or -inf for negative infinity…

Explanation:

Step1: Find the derivative

The derivative of $f(x)=x^{2}-6x + 14$ using the power - rule $(x^n)'=nx^{n - 1}$ is $f'(x)=2x-6$.

Step2: Set the derivative less than 0

We want to find where $f(x)$ is decreasing, so we set $f'(x)<0$. That is $2x - 6<0$.

Step3: Solve the inequality

Add 6 to both sides: $2x<6$. Then divide both sides by 2: $x < 3$.

Answer:

$(-\infty,3)$