JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f : R \to R\) be a function such that \(\left| {f\left( x \right)} \right| \leq {x^2}\) , for all \(x \in R\) . Then, at \(x\, = 0\), \(f\) is
- A continuous but not differentiable
- B continuous as well as differentiable.
- C neither continuous nor differentiable
- D differentiable but not continuous.
Answer & Solution
Correct Answer
(B) continuous as well as differentiable.
Step-by-step Solution
Detailed explanation
Let \(\left| {f\left( x \right)} \right| \le {x^2},\forall x \in R\) Now, at \(x = 0,\left| {f\left( 0 \right)} \right| \le 0\) \( \Rightarrow f\left( 0 \right) = 0\)…
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