Question

How many critical points does the function g(x) = |1-x^2| have?​

Answer 1

Answer:

Option #1: replace |z| = sqrt(z^2)

g(x) = | 1 - x^2 | = sqrt ( (1-x^2)^2)

= ((1-x^2)^2)^(1/2)

0= g'(x) = (1/2) ((1 - x^2)^2)^(-1/2) (2(1-x^2)(-2x))

= (-2x)(1 - x^2) / ((1 - x^2)^2)^1/2

= (-2x)(1-x^2)/ (1 - x^2)

= -2x

relative max at (0,1)

think it helps you