Question

Describe the x-values at which the function y = |x² - 36| is differentiable. Enter your answer using interval notation.

Answer 1

The function y = |x² - 36| is differentiable at all x-values except x = -6 and x = 6.

Step-by-step explanation:

The function y = |x² - 36| is differentiable at all x-values except for the values that make the expression inside the absolute value equal to zero. In this case, we have x² - 36 = 0, which gives us x = ±6. Therefore, the function is not differentiable at x = -6 and x = 6. Using interval notation, the x-values at which the function is differentiable are (-∞, -6) ∪ (-6, 6) ∪ (6, ∞).