Question

Determine if the function f(x) is continuous and/or differentiable at x=4 f(x)={ll} x+12 & { for }-4 ≤ x ≤ 4 4 x & { for } 4

Answer 1

The function f(x) is continuous but not differentiable at x=4.

Step-by-step explanation:

The function f(x) is continuous at x=4 since the limit of f(x) as x approaches 4 from both sides exists and is equal to 16. However, f(x) is not differentiable at x=4 because the left and right derivatives do not agree. The left derivative is equal to 1 and the right derivative is equal to 4. Therefore, f(x) is continuous but not differentiable at x=4.