Find the absolute max and min values of the following functions on the given intervals.

Question

f(x)= x+ sqrt(1-x^2) on [-1,1]
I found the derivative to be 1+1/2(1-x^2)^-1/2*(-2x), where do I go from there?

Answer 1

you are correct.
f' = 1 - x/√(1-x^2)
f'=0 at x = 1/√2
so there is a local max at x = 1/√2
Now check f(-1) and f(1) to see whether those values are greater or less than f(1/√2)
The absolute max is the greatest of these, and the absolute min is the least.