Home
Class 12
MATHS
Let the function f(x) be defined as foll...

Let the function f(x) be defined as follows:
`f(x)={x^(3)+x^(2)-10x,-1lexle0`
`cosx,0lexlepi//2`
`1+sin x, pi//2 lexlepi`

A

a local minimum at x=`pi//2`

B

a global maximum at x=`pi//2`

C

a absolute maximum at x=-1

D

a absolute maximum at x=`pi`

Text Solution

Verified by Experts

The correct Answer is:
3
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|40 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|42 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise 6.7|5 Videos

  • METHODS OF DIFFERETIATION

    CENGAGE|Exercise Question Bank|13 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

Let the function f(x be defined as follows: f(x)={x^3+x^2-10 x ,-1lt=x<0cosx ,0lt=x

Let the function f be defined by f(x)={(3x0lexle1),(-3x+51ltxle2):} , then:

Let the function f be defined f(x)={:{(3x,0lexle1),(-3x+5,1ltxle2):} then............

A function f:[-7, 6) to R is defined as follows. f(x)={(x^(2)+2x+1, -7lexlt-5), (x+5, -5lexle2), (x-1, 2ltxlt6):} Find 2f(-4)+3f(2)

A function is defined by f(x)=2x-3 Find (f(0)+f(1))/(2) .

CENGAGE-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Exercise (Single)
  1. If f(x)={sin^(-1)(sinx),xgt0 (pi)/(2),x=0,then cos^(-1)(cosx),xlt0

    Text Solution

    |

  2. A function f is defined by f(x)=|x|^m|x-1|^nAAx in Rdot The local max...

    Text Solution

    |

  3. Let the function f(x) be defined as follows: f(x)={x^(3)+x^(2)-10x,-...

    Text Solution

    |

  4. Consider the function f:(-oo,oo)vec(-oo,oo) defined by f(x)=(x^2+a)/(x...

    Text Solution

    |

  5. F(x) = 4 tan x-tan^(2)x+tan^(3)x,xnenpi+(pi)/(2)

    Text Solution

    |

  6. Let h(x)=x^(m/n) for x in R , where +m and n are odd numbers and 0 le...

    Text Solution

    |

  7. The greatest value of the function f(x)=(sin2x)/(sin(x+pi/4)) on the i...

    Text Solution

    |

  8. The minimum value of e^(2x^2-2x+1)sin^2x is e (b) 1/e (c) 1 (d) 0

    Text Solution

    |

  9. The maximum value of x^4ehat-x^2 is e^2 (b) e^(-2) (c) 12 e^(-2) (d...

    Text Solution

    |

  10. If a^2x^4+b^2y^4=c^6, then the maximum value of x y is (a)(c^2)/(sqrt(...

    Text Solution

    |

  11. The least natural number a for which x+a x^(-2)>2AAx in (0,oo) is 1 (b...

    Text Solution

    |

  12. f(x)={4x-x^3+ln(a^2-3a+3),0lt=x<3 x-18 ,xgeq3 complete set of values ...

    Text Solution

    |

  13. f(x)={2-|x^2+5x+6|,x!=2a^2+1,x=-2T h e nt h er a ngeofa , so that f(x...

    Text Solution

    |

  14. A differentiable function f(x) has a relative minimum at x=0. Then the...

    Text Solution

    |

  15. if f(x)=4x^3-x^2-2x+1 and g(x)={min{f(t): 0<=t<=x; 0<=x<=1, 3-x : 1...

    Text Solution

    |

  16. If f: RvecRa n dg: RvecR are two functions such that f(x)+f^(x)=-xg(x)...

    Text Solution

    |

  17. If A > 0, B > 0, and A + B = pi/3 then the maximum value of tan A tan...

    Text Solution

    |

  18. If f(x)=(t+3x-x^2)/(x-4), where t is a parameter that has minimum and ...

    Text Solution

    |

  19. The least value of a for which the equation 4/(sinx)+1/(1-sinx)=a has ...

    Text Solution

    |

  20. If f(x)=-x^(3)-3x^(2)-2x+a,a in R then the real values of x satisfying...

    Text Solution

    |