Given below are two statements. STATEMENT - 1: Let f be a differentiable function…
Mathematics · JEE Main · NTA Exams — Sets, Relations and Functions
Given below are two statements.
STATEMENT - 1: Let f be a differentiable function satisfying
\(f(x+y)=f(x)+f(y)+7 x y-1\) for all x, y ∈ R and \(f^{\prime}(0)=a\), where \(0<\mathrm{a}<1\) then, \(f(x)>0\) for all x.
STATEMENT - 2: f (x) in Statement 1 is of the form \(x^{2}+a x+1\).
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 a correct explanation for Statement - 1
- Both the statements are true but Statement - 2 is not a correct explanation for Statement - 1
- Statement - 1 is true and Statement - 2 is false
- Statement - 1 is false and Statement - 2 is true
Answer
(D) Statement - 1 is false and Statement - 2 is true
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