Limits - General Aptitude - General Aptitude (GA) Previous Year Questions

Which one of the following graphs describes the function \( f(x) = e^{-x}(x^2 + x + 1) \)?

Given the following statements about a function \( f : \mathbb{R} \to \mathbb{R} \), select the right option:
P: If \( f(x) \) is continuous at \( x = x_0 \), then it is also differentiable at \( x = x_0 \).
Q: If \( f(x) \) is continuous at \( x = x_0 \), then it may not be differentiable at \( x = x_0 \).
R: If \( f(x) \) is differentiable at \( x = x_0 \), then it is also continuous at \( x = x_0 \).