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If f(x)f(x) is a differentiable function and g(x)g(x)is a double differentiable function such that |f(x)|≤1|f(x)|≤1 and f'(x)=g(x)f′(x)=g(x). If f2(0)+g2(0)=9f2(0)+g2(0)=9. Prove that there exists some c∈(–3,3)c∈(–3,3)such thatg(c).g''(c)<0
Asked by abhyudith | 06 Apr, 2020, 23:40: PM
answered-by-expert Expert Answer
If f(x) is a differentiable function and g(x)is a double differentiable function such that |f(x)|≤1 and f′(x)=g(x). If f2(0)+g2(0)=9. Prove that there exists some c∈(–3,3) such that g(c).g''(c)<0
Solution: 
TO prove: g(x).g''(x)<0 for some c∈(–3,3)
This means that one of g(x) or g"(x) is negative is negative
Let's assume that both are positive.
Since, |f(x)|≤1
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Answered by Renu Varma | 07 Apr, 2020, 16:06: PM

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