given the derivative of a continuous function, f(x) = (x^2 - 10x + 25)/(x + 8), if each of the critical…

given the derivative of a continuous function, f(x) = (x^2 - 10x + 25)/(x + 8), if each of the critical points and key values of the function were added together, their sum total would be: 0 -3 5 -8

given the derivative of a continuous function, f(x) = (x^2 - 10x + 25)/(x + 8), if each of the critical points and key values of the function were added together, their sum total would be: 0 -3 5 -8

Answer

Explanation:

Step1: Find critical - points

Critical points occur where $f'(x)=0$ or $f'(x)$ is undefined. Set $f'(x) = 0$, so $\frac{x^{2}-10x + 25}{x + 8}=0$. Since $\frac{a}{b}=0$ when $a = 0$ and $b\neq0$, set $x^{2}-10x + 25=0$. Factor $x^{2}-10x + 25=(x - 5)^{2}=0$, then $x = 5$. $f'(x)$ is undefined when $x+8=0$, so $x=-8$.

Step2: Calculate the sum

The critical points are $x = 5$ and $x=-8$. The sum of the critical points is $5+( - 8)=-3$.

Answer:

-3