Home
Class 12
MATHS
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)andh(0)=2,`
`h(1)=4,` then the equation y=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`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • TIPS

    FIITJEE|Exercise OBJECTIVE|84 Videos

  • TIPS

    FIITJEE|Exercise ASSERTION REASONING|8 Videos

  • TIPS

    FIITJEE|Exercise NUERICAL DECIMAL BASED QUATIONS|20 Videos

  • TEST PAPERS

    FIITJEE|Exercise MATHEMATICS|328 Videos

  • TRIGNOMETRIC RATIOS AND IDENTITIES

    FIITJEE|Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

Let f be a twice differentiable function such that f''(x)=-f(x), and f'(x)=g(x),h(x)=[f(x)]^(2)+[g(x)]^(2) Find h(10) if h(5)=11

If f(x) is a twice differentiable function such that f'' (x) =-f,f'(x)=g(x),h(x)=f^2(x)+g^2(x) and h(10)=10 , then h (5) is equal to

If f is twice differentiable such that f^(')(x)=-f(x) and f^(prime)(x)=g(x)dot If h(x) is twice differentiable function such that h^(prime)(x)=(f(x))^2+(g(x))^2dot If h(0)=2,h(1)=4, then the equation y=h(x) represents (a)a curve of degree 2 (b)a curve passing through the origin (c)a straight line with slope 2 (d)a straight line with y intercept equal to 2.

Let f be a twice differentiable function such that f''(x)=-f(x)" and "f'(x)=g(x)."If "h'(x)=[f(x)]^(2)+[g(x)]^(2), h(a)=8" and "h(0)=2," then "h(2)=

STATEMENT - 1 : Let f be a twice differentiable function such that f'(x) = g(x) and f''(x) = - f (x) . If h'(x) = [f(x)]^(2) + [g (x)]^(2) , h(1) = 8 and h (0) =2 Rightarrow h(2) =14 and STATEMENT - 2 : h''(x)=0

Let f be twice differentiable function such that g'(x)=-(f(x))/(g(x)),f'(x)=(g(x))/(f(x))h(x)=e^((f(x))^(2)+(g(x))^(2)+x)If h(5)=e^(6) then h(10) is equal to

Let f(x) be twice differentiablesuchthat f''(x)=-f(x),f'(x)=g(x), where f'(x) and f''(x) represent the first and second derivatives of f(x), respectively.Also if h(x)=(f(x))^(2)+(g(x))^(2) and h(5)=5 then h(10) is equal to

If f is a differentiable function of x, then lim_(h rarr0)([f(x+n)]^(2)-[f(x)]^(2))/(2h)

Let f be a differentiable function such that f(0)=e^(2) and f'(x)=2f(x) for all x in R If h(x)=f(f(x)) ,then h'(0) is equal to

FIITJEE-TIPS-ASSIGNMENT (SECTION (I): MCQ (SINGLE CORRECT)
  1. If f(x)=(tan(pi/4+(log)e x))^((log)x e) is to be made continuous at x=...

    Text Solution

    |

  2. Let g(x) = (x-1)^n/(log(cos^m(x-1))) ; 0 lt x lt 2 ,m and n and let p ...

    Text Solution

    |

  3. If f is twice differentiable such that f"(x)=-f(x) f'(x)=g(x),h'(x)=...

    Text Solution

    |

  4. lim(x->0) (tan^2[x])/([x]^2), where [] represents greatest integer fun...

    Text Solution

    |

  5. lim(xrarr1^(+))(log(sqrt2)sqrt2x)^(1/({x})) where [ ] represents great...

    Text Solution

    |

  6. The value of lim(xto(pi)/4)(4sqrt(2)-(cosx+sinx)^(5))/(1-sin2x) is

    Text Solution

    |

  7. lim(xrarrpi)([sinx]+x) is

    Text Solution

    |

  8. The slope of the tangent of the curve y=int0^x (dx)/(1+x^3) at the poi...

    Text Solution

    |

  9. The slope of the tangent to a curve y=f(x) at (x,f(x)) is 2x+1. If the...

    Text Solution

    |

  10. The difference between the greatest and the least values of the functi...

    Text Solution

    |

  11. Let f''(x) gt 0 AA x in R and g(x)=f(2-x)+f(4+x). Then g(x) is increas...

    Text Solution

    |

  12. If f(1)(x)=2x, f(2)x(=3 sin x-x cos x, for x in (0, (pi)/(2))

    Text Solution

    |

  13. Let f(x)=x^3+kx^2+5x+4sin^2x be an increasing function on x in R. Th...

    Text Solution

    |

  14. Let g'(x)gt 0 and f'(x) lt 0 AA x in R, then

    Text Solution

    |

  15. If x1 and x2 are abscissae of two points on the curve f(x) = x - x^2 i...

    Text Solution

    |

  16. f(x)={ax^2+bx+c, |x| > 1 x+1, |x| <= 1. If f(x) is continuous for all ...

    Text Solution

    |

  17. Function g(x)=int- 3^xsint(1/2-cost)dt where 0 < x < 2pi, has

    Text Solution

    |

  18. int(dx)/((x+3)^(8//7)(x-2)^(6//7)) is equal to

    Text Solution

    |

  19. If int(dx)/(sin^4x+cos^4x)=1/(sqrt(2))tan^(- 1)f(x)+C then

    Text Solution

    |

  20. int(cosalpha)/(a^2+sin^2alpha)d alpha is equal to

    Text Solution

    |