Question:
The function \(f(x) = kx – \sin x\) is strictly increasing for
फलन \(f(x) = kx – \sin x\) किसके लिए निरंतर वर्धमान (strictly increasing) है?
Options:
- k < −1
- k > −1
- k < 1
- k > 1
- k < −1
- k > −1
- k < 1
- k > 1
Correct Answer: d)
Explanation:
A function is strictly increasing if \(f'(x) > 0\).
\(f'(x) = k – \cos x > 0 \implies k > \cos x\).
Since \(\max(\cos x) = 1\), this holds for all \(x\) if \(k > 1\).
निरंतर वर्धमान होने के लिए \(f'(x) > 0\) होना चाहिए।
\(f'(x) = k – \cos x > 0 \implies k > \cos x\)।
चूँकि \(\cos x\) का महत्तम मान 1 है, अतः \(k > 1\)।