Does f(x)= 4x^2 - 4x (quadratic function) have a maximum or minimum value and what is the value?

Question

Thanks guys. I love see things worled out!!

Answer 1

No maximum (because as x outside of -1 to 1 increases, y increases rapidly)
The minimum is -1, at x=0.5.
For the moment, drop the factor 4.
Consider x^2 - x
Is x^2 greater than x? Yes, for all x > 1, and x<-1 it is. But its not for |x| in 0 to 1. The difference is highest when x = 0.5, therefore f(x) is least at x = 0.5

Answer 2

minimum: if x=1/2, y =-1

Answer 3

No, it does not.