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IMPORTANT
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The sum of lengths of the hypotenuse and another side of a right angled triangle is given. The area of the triangle will be maximum, if the angle between them is

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Important Questions on Application of Derivatives

EASY
JEE Main/Advance
IMPORTANT
Divide 64 into two parts such that sum of the cubes of two parts is minimum. The two parts are
EASY
JEE Main/Advance
IMPORTANT
If fx=x55x4+5x310 has local maximum and minimum at x=a and x=b respectively then a, b is
HARD
JEE Main/Advance
IMPORTANT
The positive real number x when added to its reciprocal gives the minimum value of the sum at x equal to:
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JEE Main/Advance
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For all a, bR, the function fx=3x4-4x3+6x2+ax+b has

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JEE Main/Advance
IMPORTANT
Maximum area of a rectangle which can be inscribed in a circle of a given radius R is
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JEE Main/Advance
IMPORTANT
If atmosphere pressure at a height of h units is given by the function Ph=heh then pressure is maximum at the height of
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JEE Main/Advance
IMPORTANT
The radius of cylinder of maximum volume which can be inscribed in a right circular cone of radius R and height H (axis of cylinder and cone are same) H given by
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JEE Main/Advance
IMPORTANT
Let fx=x2    ; x3x22x4  ; x>3 Then the number of critical points on the graph of the function is