To do it analytically, get rid of the absolute value: How do you find the critical value of a absolute value function?
To obtain the critical points of a function, first, we obtain the first derivative of the function.
How to find critical numbers of absolute value function. Those three points are the critical points. X 2 − 4 ≥ 0 if and only if − 2 ≤ x ≤ 2, so. Next, we set the first derivative equal to zero and solve for x.
The values of x obtained are the critical points of the function. If you look at the graph of y = | x 2 − 4 |, you’ll see that it has a horizontal tangent at x = 0, y = 4 and sharp points at x = ± 2, y = 0; Click to see full answer.