Home
Class 12
MATHS
Let h(x)=x^(m/n) for x in R , where m ...

Let `h(x)=x^(m/n)` for `x in R ,` where m and n are odd numbers where 0`<`m`<`n. Then y= h(x) has a. no local extremums b. one local maximum c. one local minimum d. none of these

A

no local extremums

B

one local maximum

C

one local minimum

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
1
`h(x) =(m)/(n)x^(m-n)/(n)=(m)/(n)x^(even)/(odd)`
As h'(x) is undefined at x=0 and h(x) does not change its sign in the neightborhood there are no extremums
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|48 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Numerical Value Type|24 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Concept Application Exercise 6.7|5 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Single Correct Answer Type|46 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=x^(m/n) for x in R where m and n are integers , m even and n odd and 0

Let f(x)=a sin x+c , where a and c are real numbers and a>0. Then f(x)lt0, AA x in R if

If (x-a)^(2m) (x-b)^(2n+1) , where m and n are positive integers and a > b , is the derivative of a function f then-

If (x-a)^(2m) (x-b)^(2n+1) , where m and n are positive integers and a > b , is the derivative of a function f then-

lf sum of maximum and minimum value of y = log_2(x^4+x^2+1) - log_2 (x^4 +x^3 +2x^2+x+1) can be expressed in form ((log_2 m)-n) , where m and n are coprime then compute (m+n) .

Verify Rolles theorem for the function f(x)=(x-a)^m(x-b)^n on the interval [a , b], where m , n are positive integers.

Let S={(x,y)|x,y in R, x^2+y^2-10x+16=0} . The largest value of y/x can be put in the form of m/n where m, n are relatively prime natural numbers, then m^2+n^2=

Let f(x) =x^(n+1)+ax^n, "where " a gt 0 . Then, x=0 is point of

Prove that (1+x)^ngeq(1+n x), for all natural number n, where x >-1.

Consider (1+x+x^(2)) ^(n) = sum _(r=0)^(2n) a_(r) x^(r) , "where " a_(0),a_(1), a_(2),…a_(2n) are real numbers and n is a positive integer. The value of a_(2) is

CENGAGE ENGLISH-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Exercise
  1. Consider the function f:(-oo,oo)vec(-oo,oo) defined by f(x)=(x^2+a)/(x...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. The minimum value of e^((2x^2-2x+1)sin^(2)x) is a. e (b) 1/e (c) 1 ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. Least natural number a for which x+ax^(-2)gt2,AAx in(0,oo) is

    Text Solution

    |

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

    Text Solution

    |

  10. 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

    |

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

    Text Solution

    |

  12. 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

    |

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

    Text Solution

    |

  14. If A gt 0, B gt 0, A+B= pi //3, and maximum value of tan A tan B is M ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. which of the following is the greatest?

    Text Solution

    |

  19. If the equation 4x^(3)+5x+k=0(k in R) has a negative real root then ...

    Text Solution

    |

  20. Tangent is drawn to ellipse (x^2)/(27)+y^2=1 at (3sqrt(3)costheta,sint...

    Text Solution

    |