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  4. The sum of all values of x for which the function f(x)=√ |x2-5 x+6| is continuous, but not differentiable is

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Q. The sum of all values of $x$ for which the function $f(x)=\sqrt{\left |x^{2}-5 x+6\right|}$ is continuous, but not differentiable is

Continuity and Differentiability

Solution:

The function is only non-differentiable where the quadratic in the absolute value is equal to zero, which occurs at $x=2$ and $x=3$.