WBJEE · Maths · Functions
Let \(f: R \rightarrow R\) be such that \(f(0)=0\) and \(\left|f^{\prime}(x)\right| \leq 5\) for all \(x\). Then \(f(1)\) is in
- A \((5,6)\)
- B \([-5,5]\)
- C \((-\infty,-5) \cup(5, \infty)\)
- D \([-4,4]\)
Answer & Solution
Correct Answer
(B) \([-5,5]\)
Step-by-step Solution
Detailed explanation
\(\left|f^{\prime}(x)\right| \leq 5\) \(\int_{0}^{1}-5 d x \leq \int_{0}^{1} f^{\prime}(x) d x \leq \int_{0}^{1} 5 d x\) \(\Rightarrow-5 \leq f(1)-0 \leq 5\) \(\Rightarrow-5 \leq f(1) \leq 5\) \(\Rightarrow f(1) \in[-5,5]\)
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