Home
Class 12
MATHS
If f(x) = {{:(3x^(2)+12x -1",",-1 le x l...

If `f(x) = {{:(3x^(2)+12x -1",",-1 le x le 2),(37 - x",",2 lt x le 3):}`, then

A

f(x) is increasing on [-1,2]

B

f(x) is continuos on [-1,3]

C

f'(x) does not exist at x=2

D

f(x) has the maximum value at x=2

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise EXAMPLE|35 Videos
  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise For Session 1|7 Videos
  • MATRICES

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

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

Similar Questions

Explore conceptually related problems

Show that the function f (x)={ {:(3x^(2) + 12 x - 1,- 1 le x le 2 ),(" "37 - x," "2 lt x le 3 ):} is continuous at x = 2

If f(x) = {{:(|1-4x^(2)|",",0 le x lt 1),([x^(2)-2x]",",1 le x lt 2):} , where [] denotes the greatest integer function, then

Let f (x) { {:(1+x"," , 0 le x le 2),( 3-x"," ,2 lt x le 3):}: Find fof.

Draw the graph of the function and discuss the continuity and differentiability at x = 1 for, f(x) = {{:(3^(x)",","when",-1 le x le 1),(4-x",","when",1 lt x lt 4):}

Consider the function f(x) = {{:(x{x}+1",","if",0 le x lt 1),(2-{x}",","if",1 le x le 2):} , where {x} denotes the fractional part function. Which one of the following statements is not correct ?

Let f(x)={(x+1",", x lt1),(2x+1",",1lt x le 2):}" and " g(x)={(x^(3)",", -1 le x lt 2),(x+2",",2 le x le 3):} find fog(x) .

Show that the function f(x) = {{:(2x+3",",-3 le x lt -2),(x+1",",-2 le x lt 0),(x+2",",0 le x le 1):} is discontinuous at x = 0 and continuous at every point in interval [-3, 1]

Determine the values of x for which the following functions fails to be continuous or differentiable f(x) = {{:((1-x)",",x lt 1),((1-x)(2-x)",",1 le x le 2),((3-x)",",x gt 2):} justify your answer.

Let f(x) = x^(3) - x^(2) + x + 1 and g(x) = {{:(max f(t)",", 0 le t le x,"for",0 le x le 1),(3-x",",1 lt x le 2,,):} Then, g(x) in [0, 2] is a. continuous for x in [0, 2] - {1} b. continuous for x in [0, 2] c. differentiable for all x in [0, 2] d. differentiable for all x in [0, 2] - {1}

ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If f(x) = {{:(3x^(2)+12x -1",",-1 le x le 2),(37 - x",",2 lt x le 3):}...

    Text Solution

    |

  2. The least value of alpha in R for which 4ax^2+(1)/(x)ge1, for all xgt ...

    Text Solution

    |

  3. The number of points in (-oo,oo), for which x^2-xsinx-cosx=0, is

    Text Solution

    |

  4. Let f : R ->(0,oo) and g : R -> R be twice differentiable functions...

    Text Solution

    |

  5. Let f:(0,oo) to vec R be given by f(x)=int(1/x)^x(e^(-(t+1/t))dt)/t , ...

    Text Solution

    |

  6. The fuction f(x)=2|x|+|x+2|-||x+2|-2|x|| has a local minimum or a loca...

    Text Solution

    |

  7. A rectangular sheet of fixed perimeter with sides having their lengths...

    Text Solution

    |

  8. A vertical line passing through the point (h,0) intersects th ellipse ...

    Text Solution

    |

  9. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

  10. The total number of local maxima and local minima of the function f(x)...

    Text Solution

    |

  11. If the function g:(-oo,oo)->(-pi/2,pi/2) is given by g(u)=2tan^-1(e^u)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |