Home
Class 12
MATHS
Show that sin^(P) theta cos^(q) theta at...

Show that `sin^(P) theta cos^(q) theta` attains a maximum value, when `theta = tan^(-1) sqrt((p)/(q))`.

Text Solution

Verified by Experts

The correct Answer is:
`rArr" "tan theta = +- sqrt((p)/(q))`
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    ARIHANT PUBLICATION|Exercise QUESTION FOR PRACTICE PART - IV (LONG ANSWER TYPE QUESTIONS)|11 Videos
  • APPLICATION OF DERIVATIVES

    ARIHANT PUBLICATION|Exercise QUESTION FOR PRACTICE PART - V (VERY SHORT ANSWER TYPE QUESTIONS )|6 Videos
  • APPLICATION OF DERIVATIVES

    ARIHANT PUBLICATION|Exercise QUESTION FOR PRACTICE PART - IV (VERY SHORT ANSWER TYPE QUESTIONS)|7 Videos
  • AREA UNDER PLANE CURVES

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE (LONG ANWER TYPE QUESTIONS)|15 Videos

Similar Questions

Explore conceptually related problems

Evaluate : int (d theta)/(4cos^2 theta + 9 sin^2 theta)

If x=2cos theta-cos 2theta and y=2sin theta-sin 2 theta , then prove that (dy)/(dx)=tan((3theta)/(2))

Solve the following: cos 2theta - cos theta = sin theta - sin 2theta

Find the slope of the normal to the curve x = a cos^(3) theta and y = a sin^(3) theta "at" theta = (pi)/(4)

Prove that tantheta(1+sec2theta)=tan2theta

An isosceles triangle of vertical angle 2 theta is inscribed in a circle of radius a. Show that the area of triangle is maximum when theta = (pi)/(6) .

Prove that: y = (4 sin theta)/(2 +cos theta)- theta is an increasing function in [0,pi/2]

If A = cos^2theta + sin^4theta then prove that for all values of theta, (3)/4 leAle1.

ARIHANT PUBLICATION-APPLICATION OF DERIVATIVES -QUESTION FOR PRACTICE PART - IV (SHORT ANSWER TYPE QUESTIONS )
  1. Find all the points of local maxima and local minima of the function ...

    Text Solution

    |

  2. Find the number of local maxima and local minima points in f(x) = 2x^(...

    Text Solution

    |

  3. Show that (x^(5) - 5x^(4) + 5x^(3) - 1) has local maximum value when x...

    Text Solution

    |

  4. Find the points at which the function f given by f(x) = (x - 2)^(4) (x...

    Text Solution

    |

  5. Find the maximum and minimum values, if any of the following functions...

    Text Solution

    |

  6. Find the local maximum and local minimum values of ((x - 1)(x-6))/(x-1...

    Text Solution

    |

  7. Find the local maximum and local minimum values of the function f(x) =...

    Text Solution

    |

  8. Prove that the maximum value of ((1)/(x))^(x)"is e"^((1)/(e)).

    Text Solution

    |

  9. Find the point of local maxima and local minima of the function f(x) =...

    Text Solution

    |

  10. Find the local maximum and local minimum value of the function f(x) ...

    Text Solution

    |

  11. Find the maximum and minimum values of f(x) = sec x + log cos^(2)x, 0 ...

    Text Solution

    |

  12. Show that sin^(P) theta cos^(q) theta attains a maximum value, when th...

    Text Solution

    |

  13. Find the absolute maximum and minimum values of f(x) = 2x^(3) - 24x + ...

    Text Solution

    |

  14. Find the difference between the greatest and least values of the funct...

    Text Solution

    |

  15. Find the absolute maximum and absolute minimum values of the function ...

    Text Solution

    |

  16. Find two positive numbers whose sum is 16 and the sum of whose squares...

    Text Solution

    |

  17. Prove that the largest rectangle with a given perimeter is a square.

    Text Solution

    |