let g(x) = abs( cosx-1), The max. value attained by g on closed interval [0, 2pi] is for x equal to?

Question

abs= absolute value.

Answer 1

the range of cosine is [-1,1], so that shifting it down will make the range of cosx-1 to be [-2,0].

Taking the absolute value gives you the max value of the function at 2.

Answer 2

g(x) = abs( cosx-1)

[0, 2pi] let's
-1 <= cosx <= 1
-2 <= cosx - 1 <= 0
0 <= | cosx - 1 | <= 2
0 <= g(x) <= 2
max is 2 ^-^

Answer 3

Since we have absolute values, cos x can equal
-1, and the arguement becomes (-2). This happens at pi radians.