Question:
The function $f(x)=|x^{2}-3x+2|,x\in\mathbb{R}$ is not differentiable at ________.
The function $f(x)=|x^{2}-3x+2|,x\in\mathbb{R}$ is not differentiable at ________.
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Absolute value functions of polynomials are non-differentiable at their simple roots.
Updated On: Jun 26, 2026
- $x=1$ and $x=3$
- $x=1$ and $x=2$
- $x=2$ and $x=4$
- $x=4$ and $x=5$
- $x=-1$ and $x=-2$
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The Correct Option is B
Solution and Explanation
Step 1: Concept
$|g(x)|$ is generally not differentiable where $g(x)=0$ if $g'(x) \ne 0$ at those points.
Step 2: Meaning
Set $x^2-3x+2 = 0 \implies (x-1)(x-2) = 0$.
Step 3: Analysis
The roots are $x=1$ and $x=2$. These are the points where the graph has "sharp corners".
Step 4: Conclusion
The function is not differentiable at $x=1$ and $x=2$. Final Answer: (B)
$|g(x)|$ is generally not differentiable where $g(x)=0$ if $g'(x) \ne 0$ at those points.
Step 2: Meaning
Set $x^2-3x+2 = 0 \implies (x-1)(x-2) = 0$.
Step 3: Analysis
The roots are $x=1$ and $x=2$. These are the points where the graph has "sharp corners".
Step 4: Conclusion
The function is not differentiable at $x=1$ and $x=2$. Final Answer: (B)
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