find the absolute maximum and minimum values of the function over the indicated interval.\nf(x)=2x² +…

find the absolute maximum and minimum values of the function over the indicated interval.\nf(x)=2x² + 3\n(a)3,6 (b)-6,6\n(a) the absolute maximum value is □ at x=□\n(use a comma to separate answers as needed.)

find the absolute maximum and minimum values of the function over the indicated interval.\nf(x)=2x² + 3\n(a)3,6 (b)-6,6\n(a) the absolute maximum value is □ at x=□\n(use a comma to separate answers as needed.)

Answer

Explanation:

Step1: Analyze the function (y = 2x^{2}+3)

The function (y = 2x^{2}+3) is a parabola. The general form of a parabola is (y = ax^{2}+bx + c), here (a = 2), (b = 0), (c = 3). Since (a=2>0), the parabola opens upwards. The vertex of the parabola (y = ax^{2}+bx + c) is at (x=-\frac{b}{2a}). Substituting (a = 2) and (b = 0), we get (x = 0). But for the interval ([3,6]):

Step2: Evaluate the function at the endpoints of the interval ([3,6])

When (x = 3), (y=f(3)=2\times3^{2}+3=2\times9 + 3=18 + 3=21). When (x = 6), (y=f(6)=2\times6^{2}+3=2\times36+3=72 + 3=75).

Answer:

The absolute maximum value is (75) at (x = 6)