Question

Let \( f(x) = x^2 \log(\cos x) \log(1 + x) \) for \( x \neq 0 \), and \( f(0) = 0 \). Determine the behavior of \( f(x) \) at \( x = 0 \).

• A. not continuous
• B. continuous but not differentiable
• C. differentiable
• D. not continuous, but differentiable

Hint:

To check if a function is differentiable at a point, verify both its continuity and the existence of the derivative at that point.