Home
Class 12
MATHS
Leg f(x)=x^4-4x^3+6x^2-4x+1. Then, f inc...

Leg `f(x)=x^4-4x^3+6x^2-4x+1.` Then, `f` increase on `[1,oo]` `f` decreases on `[1,oo]` `f` has a minimum at `x=1` `f` has neither maximum nor minimum

A

f increases on `[1,oo]`

B

f decreases on `[1,oo]`

C

f has a minimum at x=1

D

f has neither maximum nor minimum

Text Solution

Verified by Experts

The correct Answer is:
1,3
f(x)=`4(x^(3)=3x^(2)+3x-1)=4(x-1)^(3)gt0 for x gt1`
Hence f increases in `[1,oo)` Moreover f(x)`lt0 for x lt 1`
Hence f has a minimum at x =1
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|42 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Linked comprehension type|8 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise (Single)|93 Videos

  • METHODS OF DIFFERETIATION

    CENGAGE|Exercise Question Bank|29 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

Leg f(x)=x^(4)-4x^(3)+6x^(2)-4x+1. Then,f increase on [1,oo]f decreases on [1,oo]f has a minimum at x=1f has neither maximum nor minimum

Let f(x)=x^(3)+3x^(2)-9x+2. Then,f(x) has a maximum at x=1 (b) a minimum at x=1( c) neither a maximum nor a minimum at x=-3(d) none of these

If f(x)=|x|+|x-1|+|x-2| then which one of the following is not correct? (A) f(x) has a minimum at x=1 (B) f(x) has a minimum at x=0 (C) f(x) has neither a maximum nor a minimum at x=0 (D) f(x) has neither a maximum nor a minimum at x=2

Consider the function f:(-oo,oo)vec(-oo,oo) defined by f(x)=(x^2+a)/(x^2+a),a >0, which of the following is not true? maximum value of f is not attained even though f is bounded. f(x) is increasing on (0,oo) and has minimum at ,=0 f(x) is decreasing on (-oo,0) and has minimum at x=0. f(x) is increasing on (-oo,oo) and has neither a local maximum nor a local minimum at x=0.

L e tf(x)=x^3-x^2+12 x-3x=2,f(x)h a s 2ans1. Let f(x)=x-x+12x-3 thenx=2, f(x) has1) a maximum 2) a minimum3) both a maximum and a minimum4 neither a maximum nor a minimum

At x=-1 ,the function f(x)=2x^(3)-3x^(2)-12x+12 is O maximum O minimum O neither maximum nor minimum O increasing

If f(x)=2x+cot^(-1)x+log(sqrt(1+x^(2))-x) then f(x)( a)increase in (0,oo)( b)decrease in [0,oo]( c)neither increases nor decreases in [0,oo]( d) increase in (-oo,oo)

Let f(x)=|x^(2)-3x-4|,-1<=x<=4 Then f(x) is monotonically increasing in [-1,(3)/(2)]f(x) monotonically decreasing in ((3)/(2),4) the maximum value of f(x) is (25)/(4) the minimum value of f(x) is 0

CENGAGE-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Exercise (Multiple)
  1. Let f(x) = {{:(x^(2) + 3x",", -1 le x lt 0),(-sin x",", 0 le x lt pi//...

    Text Solution

    |

  2. Leg f(x)=x^4-4x^3+6x^2-4x+1. Then, f increase on [1,oo] f decreases o...

    Text Solution

    |

  3. Let f(x)=2x-sin x and g(x)=3sqrt(x). Then

    Text Solution

    |

  4. Show that f(x) = 2x + cot^-1 x + log(sqrt(1+x^2)-x) is increasing in R

    Text Solution

    |

  5. Let f(x)=|x^(2)-3x-4|,-1lexle4. Then

    Text Solution

    |

  6. If f(x)=int0^x (sint)/(t)dt,xgt0, then

    Text Solution

    |

  7. The values of parameter a for which the point of minimum of the functi...

    Text Solution

    |

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

    Text Solution

    |

  9. The function y=(2x-1)/(x-2),(xne 2)

    Text Solution

    |

  10. Let f(x) =ax^(2) + bx + c and f(-1) lt 1, f(1) gt -1, f(3) lt -4 and a...

    Text Solution

    |

  11. If f(x)=x^3-x^2+100x+2002 ,t h e n f(1000)>f(1001) f(1/(2000))>f(1...

    Text Solution

    |

  12. If f'(x) = g(x) (x-a)^2, where g(a) != 0 and g is continuous at x = a,...

    Text Solution

    |

  13. The value of a for which the function f(x)=(4a-3)(x+log5)+2(a-7)cotx/2...

    Text Solution

    |

  14. Let f(x) = (x^2 - 1)^(n+1) + (x^2 + x + 1). Then f(x) has local extrem...

    Text Solution

    |

  15. Let f(x)=sinx+ax+b.Then which of the following is/are true?

    Text Solution

    |

  16. The function (sin(x+a))/(sin(x+b)) has no maxima or minima if b-a=npi...

    Text Solution

    |

  17. Consider f(x)=ax^(4)+cx^(2)+dx+e has no point o inflection Then which ...

    Text Solution

    |

  18. L e tf(x)={((x-1)(6x-1))/(2x-1),ifx!=1/2 0,ifx=1/7 Then at x=1/2, whi...

    Text Solution

    |

  19. In which of the following graphs is x =c point of inflection?

    Text Solution

    |

  20. Let f(x) be an increasing function defined on (0,oo) . If f(2a^2+a+1)>...

    Text Solution

    |