WBJEE · Maths · Continuity and Differentiability
Let \(f(x)=\left\{\begin{array}{ll}\int_{0}^{x}|1-t| d t, & x>0 \\ x-\frac{1}{2}, & x \leq 1\end{array} .\right.\) Then
- A \(f(x)\) is continuous at \(x=1\)
- B \(f(x)\) is not continuous at \(x=1\)
- C \(f(x)\) is differentiable at \(x=1\)
- D \(f(x)\) is not differentiable at \(x=1\)
Answer & Solution
Correct Answer
(D) \(f(x)\) is not differentiable at \(x=1\)
Step-by-step Solution
Detailed explanation
Given. \(f(x)=\left\{\begin{aligned} \int_{0}^{x}|1-t| d t, & x>1 \\ x-\frac{1}{2}, & x \leq 1 \end{aligned}\right.\) Now, for \(x>1\), \(\int_{0}^{x}|1-t| d t\)…
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