Home
Class 12
MATHS
Find the intervals in which f(x)=x^3-6x^...

Find the intervals in which `f(x)=x^3-6x^2-36 x+2` is increasing or decreasing.

A

`(6,oo)`

B

`(-oo,-2)`

C

`(-2,6)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Given, `f(x)=x^(3)-6x^(2)-36x+2`
`f'(x)=3x^(2)-12x-36`
For decreasing, `f'(x) lt 0`
`rArr 3(x^(2)-4x-12) lt 0`
`rArr (x-6)(x+2) lt 0`
`rArr -2 lt x lt 6`
`rArr x in (-2,6)`
Promotional Banner

Topper's Solved these Questions

  • PRACTICE SET 15

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PAPER 2 (MATHEMATICS)|50 Videos

  • PRACTICE SET 17

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MATHEMATICS|50 Videos

Similar Questions

Explore conceptually related problems

Find the intervals in which f(x)=x^(3)-6x^(2)-36x+2 is increasing or decreasing.

Find the intervals in which f(x)=x^(3)-6x^(2)+9x+15 is increasing or decreasing.

Find the intervals in which f(x)=2x^(3)-15x^(2)+36x+1 is increasing or decreasing.

Find the intervals in which f(x)=x^(3)-12x^(2)+36x+17 is increasing or decreasing.

Find the intervals in which f(x)=2x^(3)-9x^(2)+12x-5 is increasing or decreasing.

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

Find the intervals in which f(x)=2x^(3)-24x+107 is increasing or decreasing.

Find the intervals in which f(x)=5+36x+3x^(2)-2x^(3) is increasing or decreasing.

Find the intervals in which f(x)=8+36x+3x^(2)-2x^(3) is increasing or decreasing.

Find the intervals in which f(x)=6+12x+3x^(2)-2x^(3) is increasing or decreasing.

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 16-Paper - 2 (MATHEMATICS )
  1. In the adjoining circuit, the output s is

    Text Solution

    |

  2. The slope of tangent at (x,y) to a curve passing through (2, 1) is (x...

    Text Solution

    |

  3. The value of the integral int3^6 sqrtx/(sqrt(9-x)+sqrtx)dx is

    Text Solution

    |

  4. Find the probability that a leap year will have 53 Friday or 53 Sat...

    Text Solution

    |

  5. The function f(x)=x/2+2/x has a local minimum at x=2 (b) x=-2 x=0 (...

    Text Solution

    |

  6. Two person A and B take turns in throwing a pair of dice. The first pe...

    Text Solution

    |

  7. The dr. of normal to the plane through (1,0,0), (0,1,0) which makes an...

    Text Solution

    |

  8. If twice the 11th term of an AP is equal to 7 times its 21st term, the...

    Text Solution

    |

  9. if a G.P (p+q)th term = m and (p-q) th term = n , then find its p th t...

    Text Solution

    |

  10. If x=2+a+a^2+oo,w h e r e|a|<1a n dy=1+b+b^2+oo,w h e r e|b|<1. prove ...

    Text Solution

    |

  11. 26, The distance between the lines 3x + 4y = 9 and 6x + 8y + 15-0 is 3...

    Text Solution

    |

  12. The image of the origin with reference to the line 4x+3y -25=0 is

    Text Solution

    |

  13. If g(x)="min"(x,x^(2)), where x is a real number, then

    Text Solution

    |

  14. If sin3theta = sintheta, how many solutions exist such that -2piltthet...

    Text Solution

    |

  15. If the mean and variance of a random variable X having a binomial dist...

    Text Solution

    |

  16. If the area bounded by the curve y= sin ax, y = 0, x=pi//a and x=pi //...

    Text Solution

    |

  17. The shortest distance between the lines (x-2)/(3)=(y+3)/(4)=(z-1)/(5) ...

    Text Solution

    |

  18. int e^(x log a) e^(x) dx is equal to

    Text Solution

    |

  19. Find the intervals in which f(x)=x^3-6x^2-36 x+2 is increasing or decr...

    Text Solution

    |

  20. A line with positive diection cosines passes through the ont P(2,-1,2)...

    Text Solution

    |