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

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS ENGLISH|Exercise MAXIMA AND MINIMA EXERCISE 6|2 Videos
  • MATRICES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|49 Videos
  • PAIR OF STRAIGHT LINES

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

ARIHANT MATHS ENGLISH-MONOTONICITY MAXIMA AND MINIMA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If the function g:(-oo,oo)->(-pi/2,pi/2) is given by g(u)=2tan^-1(e^u)...

    Text Solution

    |

  2. The second degree polynomial f(x), satisfying f(0)=o, f(1)=1,f'(x)gt...

    Text Solution

    |

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

    Text Solution

    |

  4. 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

    |

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

    Text Solution

    |

  6. If f(x)=e^(1-x) then f(x) is

    Text Solution

    |

  7. The maximum value of (cosalpha(1))(cos alpha(2))...(cosalpha(n)), un...

    Text Solution

    |

  8. If f(x) = {{:(e ^(x),,"," 0 le x lt 1 ,, ""), (2- e^(x - 1),,"," 1 lt ...

    Text Solution

    |

  9. If f(x) is a cubic polynomil which as local maximum at x=-1 . If f(2)=...

    Text Solution

    |

  10. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |

  11. about to only mathematics

    Text Solution

    |

  12. Find a point on the curve x^2 + 2y^2 = 6, whose distance from the li...

    Text Solution

    |

  13. Let I RvecI R be defined as f(x)=|x|++x^2-1|dot The total number of po...

    Text Solution

    |

  14. Let p(x) be a real polynomial of least degree which has a local maximu...

    Text Solution

    |

  15. Let f be a function defined on R (the set of all real numbers) such th...

    Text Solution

    |

  16. The maximum value of the expression (1)/(sin ^(2) theta + 3 sin thet...

    Text Solution

    |

  17. The maximum value of the function f(x)=2x^3-15 x^2+36 x-48 on the set ...

    Text Solution

    |

  18. A wire of length 2 units is cut into two parts which are bent respecti...

    Text Solution

    |

  19. If x =-1 and x=2 ar extreme points of f(x) =alpha log|x|+betax^(2)+x ,...

    Text Solution

    |

  20. Let a , b in R be such that the function f given byf(X) = ln |x|+bx^(2...

    Text Solution

    |