Home
Class 12
MATHS
The minimum vallue of f(x) = sin^(4)x +...

The minimum vallue of `f(x) = sin^(4)x + cos^(4)x, 0 le x le pi/2` is

A

`1/(2sqrt2)`

B

(1/4)

C

(-1/2)

D

(1/2)

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MATRICES AND DETERMINANTS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|367 Videos
  • MEASUREMENT OF ANGLES, TRIGONOMETRIC RATIOS AND RELATION BETWEEN SIDES AND ANGLES OF A TRIANGLE

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|251 Videos

Similar Questions

Explore conceptually related problems

The maximum value of f(x) = 2x^(3) -21 x^(2) +36x +20 in 0 le x le 2

Find the intervals in the function f is given by f(x) = sin x + cos x, 0 le x le 2pi is strictly increasing or strictly decreasing.

The minimum value of z = 6x + 4y subjected to 2x + 3y le 30, 3x + 2y le 24, x + 4y le 3, x,y le 0

If alpha le 2 sin^(-1) x + cos^(-1) x le beta , then

Find the number of solutions of cos x =|1+ sin x |, 0 le x le 3 pi

Find the set of values of x , which satisfy sin x * cos^(3) x gt cos * sin^(3) x , 0 le x le 2pi .

solve the differential equation (dy)/(dx) +y sec x = tan x, 0 le x le pi/2

The number of real solution of the equation sqrt(1 + cos 2x) = sqrt2 sin^(-1) (sin x), -pi le x le pi , is

HIMALAYA PUBLICATION-MAXIMA AND MINIMA-QUESTION BANK
  1. 2x^(3)-6x+5 is an increasing function, if

    Text Solution

    |

  2. If x-2y = 4, then the minimum value of xy is

    Text Solution

    |

  3. The minimum vallue of f(x) = sin^(4)x + cos^(4)x, 0 le x le pi/2 is

    Text Solution

    |

  4. If ab = 2a + 3b, a gt 0, b gt 0, then the minimum value of ab is

    Text Solution

    |

  5. Maximum slope of the curve y=-x^(3)+3x^(2)+9x-27 is :

    Text Solution

    |

  6. Function f(x) = (lambda sin x + 6 cos x)/(2 sin x + 3 cos x) is monoto...

    Text Solution

    |

  7. The function f(x) = a sin x + 1/3 sin 3x has a maximum value of x = p...

    Text Solution

    |

  8. If a lt 0, the function f(x)=e^(ax)+e^(-ax) is decreasing for all valu...

    Text Solution

    |

  9. If p and q are positive real numbers such that p^(2)+q^(2)=1 then the ...

    Text Solution

    |

  10. On the interval [0,1] the function x^(25)(1-x)^(75) takes its maximum ...

    Text Solution

    |

  11. Let P(x)=a(0)+a(1)x^(2)+a(2)x^(4)+a(3)x^(6)+……+a(n)x^(2n) be a polynom...

    Text Solution

    |

  12. The function f(x) = int1^(x) [2(t-1)(t-2)^(3)+3(t-1)^(2)(t-2)^(2)] dt ...

    Text Solution

    |

  13. Let, f(x) = int e^(x) (x-1)(x-2) dx, then f(x) decreases in the interv...

    Text Solution

    |

  14. If f(x) = xe^(x(1-x), then f(x) is

    Text Solution

    |

  15. The number of values of x where the function f(x) = cos x + cos (sqrt2...

    Text Solution

    |

  16. If f: R rarr R is defined by f(x)=(x)/(x^(2)+1) find f(f(2))

    Text Solution

    |

  17. The function f(x)=tan^(-1)(sinx+cosx) is an increasing function in :

    Text Solution

    |

  18. Suppose the cubic x^(3)-px+q has three distinct real roots, where p gt...

    Text Solution

    |

  19. The condition f(x) = x^(3)+px^(2)+qx+r (x in R) to have no extreme val...

    Text Solution

    |

  20. If m and M respectively the minimum and maximum of f(x)=(x-1)^(2)+3 fo...

    Text Solution

    |