If f is twice differentiable such that f”(x)=-f(x

Question

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) representsA.curve of degree 2B.curve passing through originC.a straight line with slope 2D.a straight line with slope -2

Nandana · Accepted Answer

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 . . .

Differential Calculus> If f is twice differentiable such that f”...

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

Amit , 9 Years ago

Nandana

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Differential Calculus> If f is twice differentiable such that f”...

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) representsA.curve of degree 2B.curve passing through originC.a straight line with slope 2D.a straight line with slope -2

Amit , 9 Years ago

Nandana

LIVE ONLINE CLASSES

Other Related Questions on differential calculus

the diameter of a roller is 84 cm and its length is 120 cm. it takes 500 complete revolution to move once over to level a playground. find the area of the playground in square m?

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Find dy/DX when y=x^sinx+sin-1√x. Please give me the solution of this problem.

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differential calculus

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
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Find dy/DX when y=x^sinx+sin-1√x.

Please give me the solution of this problem.

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where A + B + C = T
(ii) In a plane triangle ABC, find the maximum value of cosA cosB cosC.