Based on the extreme value theorem what is the maximum value of f(x)=-x^2+6x over the interval [1,4]?

Question

Answer choices are 3, 5, 8, and 9

Answer 1

maximum value of f(x)=-x^2+6x over the interval [1,4]?

The extreme value theorem say there is a minimum and a maximum over an interval for a continuous function.

f(1) = 5

f(2) = 8

f(3) = 9 Maximum Value

f(4) = 8

f(5) = 5

If you plot f(x) it is a parabola that opens downward, and using geometry to find the axis symmetry, it yields the same Maximum Value.