Home
Class 12
MATHS
The function f(x)=x^2(x-2)^2...

The function `f(x)=x^2(x-2)^2`

A

f(x) is decreasing on `(-1,1)` and has a local minimum at x=1.

B

f(x) is increasing on `(-1,1)` and has a local maximum at x=1.

C

f(x) is increasing on `(-1,1)` but has neither a local maximum nor a local minimum at x=1.

D

f(x) is decreasing on `(-1,1)` but has neither a local maximum nor a local minimum at x=1.

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    PATHFINDER|Exercise QUESTION BANK|23 Videos

Similar Questions

Explore conceptually related problems

The function f(x)=2log(x-2)-x^2+4x+1 increases in the interval

Verify Rolle's theorem for the functions f(x)=(x-1)(x-2)^(2) " in " 1 le x le 2

The function f(x) = [x]^2-[x^2] (where [.] denotes the greatest integer function ) is discontinuous at

Find the domain and range of the function f(x)=(x^2)/(1+x^2) . Is the function one-to-one?

The points of discontinuties of the function f(x)=(x+2)/(2x^(2)-x-1) are -

Find the value of C that occurs in the conclusion of largranges's MVT in the function f(x) = x^2-2x+3 in [-2,2].

Find the domain of the function f(x) =(x^(2)+2x+1)/(x^(2)-8x+12)

If the function f(x)={((x^2-(A+2)x+A)/(x-2), "for" x ne 2),(2, "for" x = 2):} is continuous at x = 2, then

What is the domain and range of the function f(x)=(x^(2)-3x+2)/(x^(2)+x-6) . Find the limit of f(x) as x approaches 2.

The function f(x)=(2x^(2)-8)/(x-2) is undefined at x=2 . What value must be assigned to f (2) , if f (x) is to be cotinuous at x =2 ?

PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. The points on the curve 9y^(2) = x^(3) , where the normal to the curve...

    Text Solution

    |

  2. The function f(x)= 4x^2+2x+1 is increasing for?

    Text Solution

    |

  3. The function f(x)=x^2(x-2)^2

    Text Solution

    |

  4. If f(x)=|x-2|+|x-4|+|x-6|. Find the set of value of x such that f(x)...

    Text Solution

    |

  5. If f(x)=|x-2|+|x-4|+|x-6|. Find the set of value of x such that f(x)...

    Text Solution

    |

  6. At birth the body weight of a normal baby should be

    Text Solution

    |

  7. At birth the body weight of a normal baby should be

    Text Solution

    |

  8. If f(x) = is an odd periodic function with period 2, then f(4) equals

    Text Solution

    |

  9. If f(x) = is an odd periodic function with period 2, then f(4) equals

    Text Solution

    |

  10. Match List - I with List-II Let the functions defined in List - I ha...

    Text Solution

    |

  11. Match List - I with List-II

    Text Solution

    |

  12. Match List - I with List-II

    Text Solution

    |

  13. Find values of x over which the function f(x)= x^2+2 is increasing

    Text Solution

    |

  14. Lel f(x)=x^3+6x^2+ax+2 lf the largest possible interval in which f(x) ...

    Text Solution

    |

  15. The function S(x)=underset0oversetx(int)sin((pit^2)/2) dt has two cri...

    Text Solution

    |

  16. If P(x) be a polynomial of degree 3 satisfyints P(-1)=10,P(1)=-6and P(...

    Text Solution

    |

  17. A line is tangent to the cvrve f(x)=(41x^3)/3 at the point p in the fi...

    Text Solution

    |

  18. Let f(x) be an decreasing function defined on (0,oo). If f(3a^2-4a+1)g...

    Text Solution

    |

  19. The curve y=ax^3+bx^2+cx+d cut y axis at (0.5) where gradient is 3 cur...

    Text Solution

    |

  20. If tangent at point P(a,b) to the curve x^3+y^3=c^3 meet the curve agi...

    Text Solution

    |