Answer:
Differentiable on the intervals (-∞, -5) ∪ (-5 , 5) ∪ (5 , ∞)
Step-by-step explanation:
The graph will look like a W shape whose vertices are at x = -5 and x = 5. The function is not differentiable at these values.
A function is differentiable at x-values if the x-value has a corresponding y-value other than 0.
The function is differentiable at [tex](-\infty, -5)\ u\ (-5,5)\ u\ (5,\infty)[/tex]
Given that:
[tex]y = |x^2 - 25|[/tex]
To determine the values of x, we will make use of the graphical method.
See attachment for graph of [tex]y = |x^2 - 25|[/tex]
From the graph, we can see that the line of [tex]y = |x^2 - 25|[/tex] touches the x-axis at -5 and 5.
This means that the function is differentiable at all values of x except -5 and 5.
Using interval notation, this is represented as:
[tex](-\infty, -5)\ u\ (-5,5)\ u\ (5,\infty)[/tex]
Read more about differentiation at:
https://brainly.com/question/18962394-
