The values of x at which the real-valued func | vedclass

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(C) function $f(x) = |g(x)|$ is not differentiable at points where $g(x) = 0$,provided $g(x)$ is a linear or polynomial function.Given $f(x) = 7|2x +

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$-\frac{1}{2}, \frac{5}{3}$

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(C) function $f(x) = |g(x)|$ is not differentiable at points where $g(x) = 0$,provided $g(x)$ is a linear or polynomial function.Given $f(x) = 7|2x + 1| - 19|3x - 5|$.The function involves absolute value terms $|2x + 1|$ and $|3x - 5|$.The term $|2x + 1|$ is not differentiable at $2x + 1 = 0$,which gives $x = -\frac{1}{2}$.The term $|3x - 5|$ is not differentiable at $3x - 5 = 0$,which gives $x = \frac{5}{3}$.Since the function is a linear combination of these absolute value functions,it is not differentiable at the points where the expressions inside the absolute values are zero.Therefore,the function $f(x)$ is not differentiable at $x = -\frac{1}{2}$ and $x = \frac{5}{3}$.

The values of $x$ at which the real-valued function $f(x) = 7|2x + 1| - 19|3x - 5|$ is not differentiable are:

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