List of top Mathematics Questions on Continuity and differentiability asked in AP EAMCET

If \(f(x) = \begin{cases} ax^2 + bx - \frac{13}{8}, & x \le 1 \\ 3x - 3, & 1<x \le 2 \\ bx^3 + 1, & x>2 \end{cases}\)is differentiable \(\forall x \in \mathbb{R}\), then \( a - b = \)
If \( y = f(x) \) is a thrice differentiable function and a bijection, then \[ \frac{d^2x}{dy^2} \left(\frac{dy}{dx}\right)^3 + \frac{d^2y}{dx^2} = ? \]

Given the function:

\[ f(x) = \begin{cases} \frac{2x e^{1/2x} - 3x e^{-1/2x}}{e^{1/2x} + 4e^{-1/2x}}, & \text{if } x \neq 0 \\ 0, & \text{if } x = 0 \end{cases} \]

Determine the differentiability of \( f(x) \) at \( x = 0 \).

If
\[ f(x)=\max\{3-x,\;3+x,\;6\} \] is not differentiable at \(x=a\), and \(x=b\), then \(|a|+|b|=\)