Home
Class 11
MATHS
Suppose that f(x) is a quadratic express...

Suppose that `f(x)` is a quadratic expresson positive for all real `x` If `g(x)=f(x)+f^(prime)(x)+f^(prime prime)(x),` then for any real `x` (where `f^(prime)(x)` and `f^(primeprime)(x)` represent 1st and 2nd derivative, respectively).
(a)`g(x)<0` (b). `g(x)>0` (c). `g(x)=0` (d). `g(x)geq0`

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos
  • LINEAR INEQUALITIES

    CENGAGE PUBLICATION|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

Suppose that f(x) isa quadratic expresson positive for all real xdot If g(x)=f(x)+f^(prime)(x)+f^(prime prime)(x), then for any real x

If f(x)=x|x|, then prove that f^(prime)(x)=2|x|

If f(x) is a quadratic expression such that f(x) gt0 forall x in R , if g(x) is defined as g(x)=f(x)+f'(x)+f''(x), then prove g(x) gt 0 forall x in R .

If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e n(d u)/(d v) is

Let f(x+y)=f(x)dotf(y) for all xa n dydot Suppose f(5)=2a n df^(prime)(0)=3. Find f^(prime)(5)dot

If y=f(x^3),z=g(x^5),f^(prime)(x)=tanx ,a n dg^(prime)(x)=secx , then find the value of lim_(x->0)(((dy)/(dz)))/x

If f(x),g(x) and h(x) are three polynomials of degree 2, then prove that phi(x) = |[f(x),g(x),h(x)],[f ^ (prime)(x),g^(prime)(x),h^(prime)(x)],[f^(primeprime)(x),g^(primeprime)(x),h^(primeprime)(x)]| is a constant polynomial.

Let fa n dg be differentiable on R and suppose f(0)=g(0)a n df^(prime)(x)lt=g^(prime)(x) for all xgeq0. Then show that f(x)lt=g(x) for all xgeq0.

If intg(x)dx=g(x) , then evaluate intg(x){f(x)+f^(prime)(x)}dx

Let f(x)a n dg(x) be two functions which are defined and differentiable for all xgeqx_0dot If f(x_0)=g(x_0)a n df^(prime)(x)>g^(prime)(x) for all x > x_0, then prove that f(x)>g(x) for all x > x_0dot

CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. If y=(sinx)^(tanx),t h e n(dy)/(dx)= (a)(sinx)^(tanx)(1+sec^2xlogsi...

    Text Solution

    |

  2. If y=sin^(-1)(sqrt(1-x^2]) and 0 < x < 1, then find (dy)/(dx)

    Text Solution

    |

  3. Suppose that f(x) is a quadratic expresson positive for all real x If ...

    Text Solution

    |

  4. If y=cos^(-1)x ,find (d^2y)/(dx^2).

    Text Solution

    |

  5. If y^2=P(x), where P(x) is a polynomial of degree 3, then 2d/dx(y^3(d^...

    Text Solution

    |

  6. If g(x)=|(f(x+c),f(x+2c),f(x+3c)),(f(c),f(2c),f(3c)),(f'(c),f'(2c),f'(...

    Text Solution

    |

  7. If f(a)=2,f^(prime)(a)=1,g(a)=-1,g^(prime)(a)=2, then the value of li...

    Text Solution

    |

  8. If x=a(cost+tsint) and y=a(sint-tcost), find (d^2y)/(dx^2)

    Text Solution

    |

  9. Prove that (2^((log)2 1/4x)-3^((log)(27)(x^2+1)^3)-2x) /(7^(4(log)(49...

    Text Solution

    |

  10. (lim)(hvec0)((e+h)^(1n(e+h))-e)/hi s

    Text Solution

    |

  11. If (x-a)^(2)+(y-b)^(2)=c^(2), for some c gt 0, prove that ([1+((dy)/...

    Text Solution

    |

  12. if y=(x^2-1)^m , then the (2m)th differential coefficient of y is

    Text Solution

    |

  13. If function f satisfies the relation f(x)*f^(prime)(-x)=f(-x)*f^(prim...

    Text Solution

    |

  14. If y=(a+b x^(3/2))/(x^(5/4))a n dy^(prime)=0a tx=5, then the value o...

    Text Solution

    |

  15. If y=e^(acos^(-1)x),-1lt=x<1,s how t h a t (1-x^2)(d^2y)/(dx^2)-x(dy)...

    Text Solution

    |

  16. Let f(x)=(x-1)(x-2)(x-3)...(x-n),n in N ,a n d f'(n)=5040. Then the v...

    Text Solution

    |

  17. If y=((a x+b))/((x^2+c)) , then find dy/dx .

    Text Solution

    |

  18. If y=xlog"{"x/((a+b x))"}" , then show that x^3(d^2y)/(dx^2)=(x(dy)/(d...

    Text Solution

    |

  19. y=f(x), where f satisfies the relation f(x+y)=2f(x)+xf(y)+ysqrt(f(x)),...

    Text Solution

    |

  20. If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, then x^3y (dy)/(dx)= (a) 0 ...

    Text Solution

    |