Absolute Maximum

Question

Consider the function f(x)=6x^2−6x+8 ,  0≤x≤9. The absolute maximum of f(x) (on the given interval) is ________

Answer 1

This question operates on the closed interval [0,9] and so the points that could give absolute maximum must be selected from the vertex, if it's in the interval (critical point, in calculus) or from f(0) or f(9), endpoints of interval.

 

f(9) = 440      f(0) = 8     f(vertex) = f(½) which is obviously < 440

 

THE ABSOLUTE MAX is point (9,440)

Answer 2

For f(x) = ax² + bx + c, the max/min occurs at x = -b/2a.

In this case x = 1/2.

Can you calculate y?