Given below are two statements. STATEMENT -1: If f(0)=0, f^ (x) = (x+ 1+x^ 2 ) . then f…
Mathematics · JEE Main · NTA Exams — Limit, Continuity and Differentiability
Given below are two statements.
STATEMENT -1: If \(f(0)=0, f^{\prime}(x)\) = \(\ln\) \(\left(x+\sqrt{1+x^{2}}\right) .\) then f (x) is positive for all x ∈ R - {0}.
STATEMENT - 2: f (x) is increasing for x > 0 and decreasing for x < 0.
In the light of the above statements, choose the correct answer from the options given below:
- Both the statements are true and Statement - 2 is the correct explanation of Statement - 1
- Both the statements are true and Statement - 2 is not the correct explanation of Statement - 1
- Statement - 1 is true and Statement - 2 is false
- Statement - 1 is false and Statement - 2 is true
Answer
(B) Both the statements are true and Statement - 2 is not the correct explanation of Statement - 1
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