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List of top Mathematics Questions on Differential Calculus

Let \( f(x) = |x - \alpha| + |x - \beta| \), where \( \alpha, \beta \) are the roots of the equation \( x^2 - 3x + 2 = 0 \). Then the number of points in \( [\alpha, \beta] \) at which \( f \) is not differentiable is:

If \(f(x) = \begin{cases} x^2 + 3x + a, & x \leq 1  bx + 2, & x>1 \end{cases}\), \(x \in \mathbb{R}\), is everywhere differentiable, then

The value of the integral \( \int_{0}^{\pi/2} \log\left(\frac{4 + 3\sin x}{4 + 3\cos x}\right) dx \) is: