List of top Engineering Mathematics Questions on Calculus asked in AP PGECET

Let \( f: \mathbb{R} \rightarrow \mathbb{R} \) be a function such that \( f(0) = 3 \) and \( |f'(x)| \leq 2 \), \( \forall x \in \mathbb{R} \). Then \( f(2) \) lies in which of the following intervals?
The directional derivative of the function \( f(x, y) = 2x^2 + y^2 \) along a line directed from \( (0, 0) \) to \( (1, 1) \), evaluated at the point \( x = 1, y = 1 \), is ___