find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x…

find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x - values at which they occur. f(x)=4x - 9;-6,6

find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x - values at which they occur. f(x)=4x - 9;-6,6

Answer

Explanation:

Step1: Determine the function's derivative

The derivative of $f(x)=4x - 9$ is $f^\prime(x)=4$. Since $f^\prime(x)$ is a non - zero constant, there are no critical points in the open interval $(-6,6)$ (critical points occur where $f^\prime(x)=0$ or $f^\prime(x)$ is undefined).

Step2: Evaluate the function at the endpoints

Evaluate $f(x)$ at $x=-6$: $f(-6)=4\times(-6)-9=-24 - 9=-33$. Evaluate $f(x)$ at $x = 6$: $f(6)=4\times6-9=24 - 9 = 15$.

Answer:

The absolute minimum value is $-33$ and it occurs at $x=-6$. The absolute maximum value is $15$ and it occurs at $x = 6$.