Home
Class 12
MATHS
If f(x)=x^3+bx^2+cx+d and 0<b^2<c, then...

If `f(x)=x^3+bx^2+cx+d` and 0<`b^2`<`c`, then

A

f(x) is strictly increasing function

B

f(x) has a local maxima

C

f(x) is strictly decreasing function

D

f(x) is bounded

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Main (Archive)|36 Videos

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|75 Videos

  • DIFFERENTIAL EQUATIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCE (ARCHIVE )|32 Videos

Similar Questions

Explore conceptually related problems

Let f(x) = ax^3 + bx^2 + cx + d sin x . Find the condition that f(x) is always one-one function.

If f(x)=ax^(3)+bx^(2)+cx have relative extrema x = 1 and at x = 5. If int_(-1)^(1)f(x)dx=6 then :

If both the critical points of f(x) = ax^(3)+bx^(2) +cx +d are -ve then

Let f(x) = x^3 + ax^2 + bx + c and g(x) = x^3 + bx^2 + cx + a , where a, b, c are integers. Suppose that the following conditions hold- (a) f(1) = 0 , (b) the roots of g(x) = 0 are the squares of the roots of f(x) = 0. Find the value of: a^(2013) + b^(2013) + c^(2013)

Find the values of a,b,c,d, if 1,2,3,4 are the roots of x^4 +ax^3 +bx^2 +cx +d=0

For f(x)=x^(3)+bx^(2)+cx+d , if b^(2) gt 4c gt 0 and b, c, d in R , then f(x)

Let f(x) = ax^(3) + bx^(2) + cx + d, a != 0 , where a, b, c, d in R . If f(x) is one-one and onto, then which of the following is correct ?

Let f(x)=ax^3+bx^2+cx+1 has exterma at x=alpha,beta such that alpha beta 0 (c)one positive root if f(alpha) 0 (d) none of these

If 1, -2, 3 are the roots of ax^(3) + bx^(2) + cx + d = 0 then the roots of ax^(3) + 3bx^(2) + 9cx + 27d = 0 are

Consider that f : R rarr R (i) Let f(x) = x^(3) + x^(2) + ax + 4 be bijective, then find a. (ii) Let f(x) = x^(3) + bx^(2) + cx + d is bijective, then find the condition.

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS 2-JEE Advanced (Archive)
  1. If the line a x+b y+c=0 is a normal to the curve x y=1, then a >0,b >...

    Text Solution

    |

  2. If the function g:(-oo,oo)rarr(-(pi)/(2),(pi)/(2)) is given by g(u)=...

    Text Solution

    |

  3. If f(x)=x^3+bx^2+cx+d and 0<b^2<c, then

    Text Solution

    |

  4. The length of the longest interval in which the function 3sinx-4sin^3x...

    Text Solution

    |

  5. If f(x)=xe^(x(1-x)), then f'(x) is

    Text Solution

    |

  6. The function f(x)=sin^4x+cos^4x increasing if 0<x<pi/8 (b) pi/4<x<(3p...

    Text Solution

    |

  7. If f(x)=x/(sinx) \ a n d \ g(x)=x/(tanx),w h e r e \ 0ltxlt=1, then in...

    Text Solution

    |

  8. The function f(x)=(log (pi+x))/(log (e+x))," is "

    Text Solution

    |

  9. Let fa n dg be increasing and decreasing functions, respectively, from...

    Text Solution

    |

  10. Let f:(0,oo) in R be given f(x)=overset(x)underset(1//x)int e^(t+(1)...

    Text Solution

    |

  11. Let h(x)=f(x)-(f(x))^2+(f(x))^3 for every real number xdot Then (a) h ...

    Text Solution

    |

  12. Let f(X) be a polynomila of degree four having extreme values at x =1 ...

    Text Solution

    |

  13. The number of points in (-oo,oo), for which x^2-xsinx-cosx=0, is

    Text Solution

    |

  14. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

  15. The total number of local maxima and local minima of the function f...

    Text Solution

    |

  16. If f(x)=x^2+2b x+2c^2 and g(x)= -x^2-2c x+b^2 are such that min f(x...

    Text Solution

    |

  17. The maximum value of (cos alpha(1))(cos alpha(2))... ( cos alpha(n)) u...

    Text Solution

    |

  18. If f(x)=(x^2-1)/(x^2+1) . For every real number x , then the minimum v...

    Text Solution

    |

  19. If f(x)=a(0)+a(1)x^(2)+a(2)x^(4)+...+ a(n)x^(2n) be a polynomial where...

    Text Solution

    |

  20. The funciton f(X) =2|x|+|x+2|-||x+2|-|x|| has a local mimimum or a lo...

    Text Solution

    |