Home
Class 12
MATHS
For the cubic function f(x)=2x^3+9x^2+12...

For the cubic function `f(x)=2x^3+9x^2+12 x+1,` which one of the following statement/statements hold good? `f(x)` is non-monotonic. `f(x)` increases in `(-oo,-2)uu(-1,oo)` and decreases in `(-2,-1)` `f: RvecR` is bijective. Inflection point occurs at `x=-3/2dot`

A

f(x) is increasing

B

Increasing in `(-oo,-2) cup (-1, oo) and ` decreasing in (-2,-1)

C

f(x) is decreasing

D

f(x) is constant

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    AAKASH INSTITUTE|Exercise Assignment SECTION-B( Objective Type Questions ( One option is correct ))|31 Videos
  • APPLICATION OF DERIVATIVES

    AAKASH INSTITUTE|Exercise Assignment SECTION-C( Objective Type Questions ( More than one option are correct ))|1 Videos
  • APPLICATION OF DERIVATIVES

    AAKASH INSTITUTE|Exercise TRY YOURSELF|39 Videos
  • APPLICATION OF INTEGRALS

    AAKASH INSTITUTE|Exercise Assignment Section - I Aakash Challengers Questions|2 Videos

Similar Questions

Explore conceptually related problems

For the cubic function f(x)=2x^(3)+9x^(2)+12x+1, which one of the following statement/statements hold good? f(x) is non-monotonic.f(x) increases in (-oo,-2)uu(-1,oo) and decreases in (-2,-1)f:R rarr R is bijective.Inflection point occurs at x=-(3)/(2) .

Which one of the following statements does not hold good for the function f(x)=cos^(-1)(2x^(2)-1)?

For which interval the given function f(x)=2x^3-9x^2+12x+1 is decreasing?

A function is defined as f(x)=lim_(x rarr oo)[cos^(2n)x, if x 1 which of the following does not hold good?

The interval on which the function f(x)=-2x^(3)-9x^(2)-12x+1 is increasing is :

A continuous and differentiable function f(x) is increasing in (-oo,3/2) and decreasing in (3/2,oo) then x=3/2 is

Find the intervals in which f(x)=-2x^(3)-9x^(2)-12x+1 is increasing or decreasing.

Function f(x)=2x^(3)-9x^(2)+12x+29 is monotonically decreasing when (a) x 2( c) x>3(d)'1

AAKASH INSTITUTE-APPLICATION OF DERIVATIVES-Assignment SECTION-A (Competition Level Questions)
  1. Consider the function f(x)= x cos x - sin x , then identify the statem...

    Text Solution

    |

  2. If x=2t-3t^(2) and y=6t^(3) then (dy)/(dx) at point (-1,6) is

    Text Solution

    |

  3. For the cubic function f(x)=2x^3+9x^2+12 x+1, which one of the followi...

    Text Solution

    |

  4. The function 'f' is defined by f(x)=x^p(1-x)^q for all x\ in R , whe...

    Text Solution

    |

  5. Let h be a twice continuously differentiable positive function on an o...

    Text Solution

    |

  6. The least area of a circle circumscribing any right triangle of area S...

    Text Solution

    |

  7. If f(x)=x(1-x)^(3) then which of following is true ?

    Text Solution

    |

  8. A function y=f(x) is given by x=1/(1+t^2) and y=1/(t(1+t^2)) for all t...

    Text Solution

    |

  9. The point on the curve y^(2)=x where tangent makes 45^(@) angle with x...

    Text Solution

    |

  10. The radius of a right circular cylinder increases at a constant rate ....

    Text Solution

    |

  11. Two sides of a triangle are to have lengths 'a'cm & 'b'cm. If the tria...

    Text Solution

    |

  12. The cost function at American Gadget is C(x)=x^(3)-6x^(2)+15x (x is t...

    Text Solution

    |

  13. A particle moves along the curve y=x^(3/2) in the first quadrant in su...

    Text Solution

    |

  14. Let f(x)=ax^(2)-b|x| , where a and b are constant . Then at x=0 , f(x)...

    Text Solution

    |

  15. Find the point on the curve 9y^2=x^3, where the normal to the curve ma...

    Text Solution

    |

  16. The angle made by any tangent to the curve x=a(t+sintcost) , y=(1+sint...

    Text Solution

    |

  17. A cube of ice melts without changing its shape at the uniform rate ...

    Text Solution

    |

  18. Consider the curve represented parametrically by the equation x = t^3-...

    Text Solution

    |

  19. The point on the curve y=6x-x^(2) where the tangent is parallel to x-a...

    Text Solution

    |

  20. For the curve y=3sinthetacostheta, x=e^(theta)sintheta, 0lt=thetalt=p...

    Text Solution

    |