Question
Download Solution PDFनिम्नलिखित कथनों पर विचार करें:
1. f(x) = In x, (0, ∞) पर एक बढ़ता हुआ फलन है।
2. f(x) = ex – x (In x) (1, ∞) पर एक बढ़ता हुआ फलन है।
उपरोक्त कथनों में से कौन सा/से सही है/हैं?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFधारणा:
f(x) को बढ़ता हुआ फलन कहा जाता है यदि f'(x) 0 से अधिक है यानी, f’(x) > 0
गणना:
1. f(x) = In x
f’(x) = 1/x जो हमेशा (0, ∞) पर 0 से अधिक है।
यह कथन सही है।
2. f(x) = ex – x (In x)
f’(x) = ex – ln(x) – x (1/x)
⇒ f’(x) = ex – ln(x) – 1
= ex – (ln(x) + 1) यह मान भी हमेशा शून्य से अधिक होता है
तो, यह कथन भी सही है।
इसलिए, विकल्प (3) सही है।
Last updated on May 30, 2025
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