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)=x² - 6x - 2; 2,5 the absolute maximum value is at x =. (use a comma to separate answers as needed.)

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)=x² - 6x - 2; 2,5 the absolute maximum value is at x =. (use a comma to separate answers as needed.)

Answer

Explanation:

Step1: Find the derivative

$f'(x)=2x - 6$

Step2: Set the derivative equal to 0

$2x-6 = 0$ $2x=6$ $x = 3$

Step3: Evaluate the function at critical - point and endpoints

$f(2)=2^{2}-6\times2 - 2=4 - 12 - 2=-10$ $f(3)=3^{2}-6\times3 - 2=9 - 18 - 2=-11$ $f(5)=5^{2}-6\times5 - 2=25 - 30 - 2=-7$

Answer:

The absolute maximum value is - 7 at x = 5. The absolute minimum value is - 11 at x = 3.