Home
Class 12
MATHS
Suppose that f(x) is a quadratic express...

Suppose that `f(x)` is a quadratic expresson positive for all real `xdot` If `g(x)=f(x)+f'(x)+f''(x),` then for any real `x(w h e r ef'(x)a n df''(x)` represent 1st and 2nd derivative, respectively). a. `g(x)<0` b. `g(x)>0` c. `g(x)=0` d. `g(x)geq0`

A

`g(x)gt0`

B

`g(x)le0`

C

`g(x)ge0`

D

`g(x)lt0`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise MAXIMA AND MINIMA EXERCISE 1|1 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|19 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise For Session 5|8 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|49 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

Similar Questions

Explore conceptually related problems

Let g(x)=f(x)+f(1-x) and f''(x)<0 , when x in (0,1) . Then f(x) is

Let f(x) be polynomial function of degree 2 such that f(x)gt0 for all x in R. If g(x)=f(x)+f'(x)+f''(x) for all x, then

f'(x) = g(x) and g'(x) =-f(x) for all real x and f(5)=2=f'(5) then f^2 (10) + g^2 (10) is

Let f(x)=x^2+xg'(1)+g''(2) and g(x)=f(1).x^2+xf'(x)+f''(x), then find f(x) and g(x).

If f(x) = x+1 And g (X) = 2x, then f (g(x)) is equal to

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 the equation y=h(x) represents.

If e^f(x)= log x and g(x) is the inverse function of f(x), then g'(x) is

If 'f' is a real valued differentiable function such that f(x) f'(x) < 0 for all real x, then

Let f(x) = exp(x^3 +x^2+x) for any real number and let g(x) be the inverse function of f(x) then g'(e^3)

ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Single Option Correct Type Questions)
  1. sinx+cosx=y^2-y+a has no value of x for any value of y if a belongs to...

    Text Solution

    |

  2. Evaluate (n!)/((n-r)!) , when n = 8 , r = 6

    Text Solution

    |

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

    Text Solution

    |

  4. Let f(x)=min{1,cos x,1-sinx}, -pi le x le pi, Then, f(x) is

    Text Solution

    |

  5. Evaluate (5!)/((5 - 2)!)

    Text Solution

    |

  6. Maximum number of real solution for the equation ax^(n)+x^(2)+bx+c=0...

    Text Solution

    |

  7. Maximum number area of rectangle whose two points are are x=x(0),x=p...

    Text Solution

    |

  8. f(x)=-1+kx+k neither touches nor intecepts the curve f(x)= Iog x, then...

    Text Solution

    |

  9. f(x) is a polynomial of degree 4 with real coefficients such that f(x)...

    Text Solution

    |

  10. A curve whose concavity is directly proportional to the logarithm of i...

    Text Solution

    |

  11. f(x) = 4 tan x-tan^(2)x+tan^(3)x,xnenpi+(pi)/(2)

    Text Solution

    |

  12. f (x)= {{:(3+|x-k|"," , x le k),(a ^(2) -2 + ( sin (x -k))/((x-k))"," ...

    Text Solution

    |

  13. Let f(x) be linear functions with the properties that f(1) le f(2), f(...

    Text Solution

    |

  14. If P(x) is polynomial satisfying P(x^(2))=x^(2)P(x)andP(0)=-2, P'(3//2...

    Text Solution

    |

  15. Find the vertex and length of latus rectum of the parabola x^(2)=-4(y-...

    Text Solution

    |

  16. Let f(x)=x^(2)-2xandg(x)=f(f(x)-1)+f(5-f(x)), then

    Text Solution

    |

  17. Prove that (9!)/((9 - 3)!) = 504

    Text Solution

    |

  18. Evaluate (n!)/((n-r)!) , when n = 10 , r = 5

    Text Solution

    |

  19. Let a(1),a(2),a(n) be sequence of real numbers with a(n+1)=a(n)+sqrt(1...

    Text Solution

    |

  20. A function f is defined by f(x)=|x|^m|x-1|^nAAx in Rdot The local max...

    Text Solution

    |