Find the absolute maximum and minimum values of the function over the indicated​ interval, and indicate the​ x-values at which they occur. f(x)=x2−2x−1​; [0,4]

Question

Find the absolute maximum and minimum values of the function over the indicated​ interval, and indicate the​ x-values at which they occur. f(x)=x²−2x−1​; [0,4]

The absolute maximum value is ________ at x= _________.

​(Use a comma to separate answers as​ needed.)

Answer 1

max is f(4) = 7 at x=4

f(4) = 4^2 -2(4) -1 = 16-8-1 = 7

f(0) = -1

local extremum is when the derivative = 0, or 2x-2=0, x=1

f(1) = 1^2 -2(1) -1 = 1-2-1 =-2 = absolute & local minimum. It's an upward opening parabola where the vertex is a minimum (1,-2). No maximums except at a given interval.