on what interval is f(x)=x² - 14x + 27 decreasing? enter inf for infinity or -inf for negative infinity…
on what interval is f(x)=x² - 14x + 27 decreasing? enter inf for infinity or -inf for negative infinity. answer in interval notation. it is decreasing on the interval
Answer
Explanation:
Step1: Find the derivative
The derivative of $f(x)=x^{2}-14x + 27$ using the power - rule $(x^n)'=nx^{n - 1}$ is $f'(x)=2x-14$.
Step2: Determine where the derivative is negative
Set $f'(x)<0$. So, $2x - 14<0$. Add 14 to both sides: $2x<14$. Divide both sides by 2: $x < 7$.
Answer:
$(-\infty,7)$