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 23 at x = 3. (use a comma to separate answers as needed.) (b) 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. 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 23 at x = 3. (use a comma to separate answers as needed.) (b) the absolute maximum value is at x = . (use a comma to separate answers as needed.)

Answer

Explanation:

Step1: Analyze the function

The function $f(x)=2x^{2}+5$ is a parabola opening upwards ($a = 2>0$ in $y = ax^{2}+bx + c$, here $b = 0,c = 5$). Its vertex - form is $y=2(x - 0)^{2}+5$, and the vertex is at $(0,5)$.

Step2: Evaluate the function at endpoints for interval [-6,6]

For $x=-6$, $f(-6)=2\times(-6)^{2}+5=2\times36 + 5=72 + 5=77$. For $x = 6$, $f(6)=2\times6^{2}+5=2\times36+5=72 + 5=77$. For $x = 0$ (vertex), $f(0)=2\times0^{2}+5=5$.

Answer:

77, -6,6