Question:
Let $f(x)=10-|x-5|,\; x\in\mathbb{R}$. Then $f(x)$ is not differentiable at:
Let $f(x)=10-|x-5|,\; x\in\mathbb{R}$. Then $f(x)$ is not differentiable at:
Show Hint
To find non-differentiable points for absolute value functions, set the expression inside the absolute value to zero.
Updated On: Apr 28, 2026
- $x=10$
- $x=15$
- $x=-5$
- $x=5$
- $x=-15$
Show Solution
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The Correct Option is D
Solution and Explanation
Step 1: Concept
The function $|x-a|$ is continuous everywhere but not differentiable at $x=a$ because of the sharp corner (cusp) in its graph.
Step 2: Analysis
In $f(x) = 10 - |x-5|$, the absolute value part is $|x-5|$.
Step 3: Conclusion
The function has a "corner" at $x-5=0$, which is $x=5$. Therefore, it is not differentiable at $x=5$. Final Answer: (D)
The function $|x-a|$ is continuous everywhere but not differentiable at $x=a$ because of the sharp corner (cusp) in its graph.
Step 2: Analysis
In $f(x) = 10 - |x-5|$, the absolute value part is $|x-5|$.
Step 3: Conclusion
The function has a "corner" at $x-5=0$, which is $x=5$. Therefore, it is not differentiable at $x=5$. Final Answer: (D)
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