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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Differentiation

NTA Abhyas 2020 · Mathematics · Differentiation

If f (x) is a twice differentiable function such that f^ " (x) = -...

If f(x)isatwicedifferentiablefunctionsuchthatf \left(x\right) is a twice differentiable function such thatf^{"}\left(x\right) = - f\left(x\right),f′(x), f^{'} \left(x\right) = g \left(x\right),h(x)=f2, h \left(x\right) = f^{2}\left(x\right)+g2(x)andh+ g^{2}\left(x\right) and h\left(10\right) = 10,thenh(5)then h \left(5\right) is equal to

Options

  1. A55
  2. B1515
  3. C1010
  4. D1717

Correct answer

C. 1010

Step-by-step solution

h′h^{'}\left(x\right) = 2f ⋅ f^{'} + 2gg^{'}<br/><br />= 2f ⋅ f^{'} + 2\left(f^{'}\right)\left(f^{"}\right) ( ∵ g = f^{'} )<br/><br />= 2f ⋅ f^{'} + 2f^{'} \left(-f\right) = 0<br/><br />∴ h^{'}\left(x\right) = 0 ⇒ h\left(x\right)isaconstantfunction<br/>is a constant function<br />∴ h\left(x\right) = 10 ⇒ h\left(5\right) = 10
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