Question:medium
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:
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:
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The function \( |x - a| \) is not differentiable at \( x = a \). The sum of such functions will be non-differentiable at the zeros of the terms inside the absolute values.
Updated On: Nov 28, 2025
- \( 2 \)
- \( 0 \)
- \( 1 \)
- \( \infty \)