What is the maximum value of the function f(x) = 2x2 - 2x + 6 in the interval…

For f(x) = 2x2 - 2x + 6, the coefficient of x2 is positive, so the parabola opens upward. Its vertex is at x = -b/(2a) = 2/4 = 0.5, which gives the minimum value on the interval.

To find the maximum on the closed interval [0, 2], compare the endpoint values:

f(0) = 6 and f(2) = 8 - 4 + 6 = 10.

Therefore, the maximum value is 10.