find the absolute maximum and minimum values of the function over the indicated interval. f(x)=2x^2 + 5 (a)…

find the absolute maximum and minimum values of the function over the indicated interval. f(x)=2x^2 + 5 (a) 3,6 (b) -6,6 (a) the absolute maximum value is 77 at x = 6. (use a comma to separate answers as needed.) the absolute minimum 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. f(x)=2x^2 + 5 (a) 3,6 (b) -6,6 (a) the absolute maximum value is 77 at x = 6. (use a comma to separate answers as needed.) the absolute minimum value is at x = . (use a comma to separate answers as needed.)

Answer

Explanation:

Step1: Find the derivative

The derivative of $f(x)=2x^{2}+5$ is $f^\prime(x) = 4x$.

Step2: Find critical - points

Set $f^\prime(x)=0$, so $4x = 0$, which gives $x = 0$. But for interval (A) $[3,6]$, the critical - point $x = 0$ is not in this interval.

Step3: Evaluate the function at endpoints

For $x = 3$, $f(3)=2\times3^{2}+5=2\times9 + 5=18 + 5=23$. For $x = 6$, $f(6)=2\times6^{2}+5=2\times36+5 = 72 + 5=77$.

Answer:

23, 3