MHT CET · Maths · Application of Derivatives
If \(f(x)=k x-\sin x\) is monotonically increasing, then
- A \(k>1\)
- B \(k>-1\)
- C \(k < 1\)
- D \(k < -1\)
Answer & Solution
Correct Answer
(A) \(k>1\)
Step-by-step Solution
Detailed explanation
Since, \(f(x)=k x-\sin x\) is monotonically increasing for all \(x \in R\). Therefore,
\(
f^{\prime}(x)>0 \text { for all } x \in R
\)
\(\therefore \quad f^{\prime}(0)>0\)
\(\Rightarrow k-\cos 0>0\)
\(\Rightarrow k > 1\)
\(
f^{\prime}(x)>0 \text { for all } x \in R
\)
\(\therefore \quad f^{\prime}(0)>0\)
\(\Rightarrow k-\cos 0>0\)
\(\Rightarrow k > 1\)
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