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If f is twice differentiable such that f”(x)=-f(x), f’(x)=g(x),h’(x)=(f(x))^2+(g(x))^2 and h(0)=2,h(1)=4 then equation of h(x) represents A.curve of degree 2 B.curve passing through origin C.a straight line with slope 2 D.a straight line with slope -2

If  f is twice differentiable such that f”(x)=-f(x), f’(x)=g(x),h’(x)=(f(x))^2+(g(x))^2 and h(0)=2,h(1)=4 then equation of h(x) represents
A.curve of degree 2
B.curve passing through origin
C.a straight line with slope 2
D.a straight line with slope -2

Grade:10

1 Answers

Nandana
110 Points
4 years ago
Hi ! Amit , I ‘ve answer for your question !
here is it ---
Ans :-
  Option D :a  straightline with slope 2
 sol :-
   let’s take f(x) = sin (x) +cos (x)
    then , f’(x) = cos (x) – sin (x)
              f’‘(x) = -sin (x) – cos (x) = -(sin (x) +cos(x)) = -f(x)
              f’(x) =g(x) = cos (x) – sin (x)
              h’(x) = [2(sin^2 (x) + cos^2(x))]
                      =2
             h(x) = ∫2 = 2x + K
             h(0) = 2 = 2*0 + K => K =2
             h(x) = 2x + 2 , which is a straight line with slope +2 passes through 2
    Thanks for Asking & be free to  share your questions , looking farward for your next question . . .

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