Home
Class 12
MATHS
Let f(x)={{:(x^2+4x "," -3 le x le 0),(...

Let `f(x)={{:(x^2+4x "," -3 le x le 0),(-sin x ","0 lt x le pi//2 ),(-cos x -1 "," pi//2 lt x le pi):}`
which one of the following is not true ?

A

x=-2 is the point of global minimum

B

x=`pi` is the point of global maximum

C

f(x) is not differentiable at `x= pi/2`

D

f(x) is discontinunous at x=0

Text Solution

Verified by Experts

The correct Answer is:
A,D

If is evident from the graph of the function that options (a),(b) and (c ) are true
Promotional Banner

Topper's Solved these Questions

  • MAXIMA AND MINIMA

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|7 Videos
  • MAXIMA AND MINIMA

    OBJECTIVE RD SHARMA|Exercise Exercise|50 Videos
  • MAXIMA AND MINIMA

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos
  • MATHEMATICAL REASONING

    OBJECTIVE RD SHARMA|Exercise Chapter Test|20 Videos
  • MEASURES OF CENTRAL TENDENCY

    OBJECTIVE RD SHARMA|Exercise Chapter Test|21 Videos

Similar Questions

Explore conceptually related problems

Let f(x) = {{:(x^(2) + 3x",", -1 le x lt 0),(-sin x",", 0 le x lt pi//2),(-1 - cos x",", (pi)/(2) le x le pi):} . Draw the graph of the function and find the following (a) Range of the function (b) Point of inflection (c) Point of local minima

Let f(x) = {{:(sgn(x)+x",",-oo lt x lt 0),(-1+sin x",",0 le x le pi//2),(cos x",",pi//2 le x lt oo):} , then number of points, where f(x) is not differentiable, is/are

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

Let f(x) = {{:( x^(3) + x^(2) - 10 x ,, -1 le x lt 0) , (sin x ,, 0 le x lt x//2) , (1 + cos x ,, pi //2 le x le x ):} then f(x) has

Find the values of a and b so that the function f(x)={{:(x+asqrt2 sin x", "0 le x le pi//4),(2x cot x + b", "pi//4 le x le pi//2),(a cot 2x - b sin x", "pi//2 lt x le pi):} is continuous for 0 le x le pi .

Let f : [ 0, oo) to [ 0,3] be a function defined by f(x) = {{:(max { sin t : 0 le t le x}" , " 0 le x le pi),( 2 + cos x", " x gt pi ):} Then which of the following is true ?

OBJECTIVE RD SHARMA-MAXIMA AND MINIMA -Section I - Solved Mcqs
  1. Let f(X)=In (2x -x^2)+ sin (pix)/(2). Then which one of the following ...

    Text Solution

    |

  2. If alpha and beta respectively the minmum and minimum values of the fu...

    Text Solution

    |

  3. Let f(x)={{:(x^2+4x "," -3 le x le 0),(-sin x ","0 lt x le pi//2 ),(...

    Text Solution

    |

  4. If alpha be the number of solutions of the equation [sin x] =|x| ) and...

    Text Solution

    |

  5. Let f(x1,x2,x3,x4)=x1^2+x2^2+x3^2+x4^2-2(x1+x2+x3+x4)+10 and x1,x3 i...

    Text Solution

    |

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

    Text Solution

    |

  7. Let f be a function defined on R (the set of all real numbers) such th...

    Text Solution

    |

  8. Let f:R to R be defined by f(x)={{:(2k-2x",",ifxle-1),(2x+3",",iffxg...

    Text Solution

    |

  9. For e in (0,(5pi)/(2)) " define " f(x)= int(0)^(x) sqrt(t) sin t dt ...

    Text Solution

    |

  10. Let p(x) be a real polynomial of least degree which has a local maximu...

    Text Solution

    |

  11. Let I RvecI R be defined as f(x)=|x|++x^2-1|dot The total number of po...

    Text Solution

    |

  12. If f(x) = int(0)^(x) e^(t^2)(t-2)(t-3) dt " for all " x in (0,oo) t...

    Text Solution

    |

  13. The function f(x)=2|x|+|x+2|=||x|2|-2|x|| has a local minimum or a loc...

    Text Solution

    |

  14. Let f:[0,1] rarr R be a function . Suppose the fuction f is twice diff...

    Text Solution

    |

  15. Let f:[0,1] rarr R be a function.such that f(0)=f(1)=0 and f''(x)+f(x...

    Text Solution

    |

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

    Text Solution

    |

  17. Let f(x) be a polynomial of degree four having extreme vlaues at x=1 ...

    Text Solution

    |

  18. A cylindrica container is to be made from certain solid material with ...

    Text Solution

    |

  19. The minimum value of the function f(x)=x^(3//2)+x^(-3//2)-4(x+1/x) ...

    Text Solution

    |

  20. The least value of a in RR for which 4ax^2+1/x >= 1, for all x > 0, ...

    Text Solution

    |