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If the sum of the lengths of the hypotenuse and another side of a right-angled triangle is given, show that the area of the triangle is maximum when the angle between these sides is `pi/3dot`

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MOTION-MAXIMA AND MINIMA -EXERCISE - 3
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  2. A wire of length 20m is to be cut into two pieces. One of the places ...

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  3. Show that the semi-vertical angle of the cone of the maximum volume a...

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  8. Find the locus of the foot of the perpendicular drawn from the cent...

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  10. Determine A and B so that y = = A/x+ Bx has a minimum at the point (1,...

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  11. Find the points of local maxima/minima of function f (x) = 2x^(3) -...

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  12. Find the points of local maxima/minima of function f(x) = - (x - 1)^...

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  13. Find the points of local maxima/minima of function f(x) = x ln x

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  14. Let f(x) = {{:( 2 sin x ,, x gt 0) , ( x^(2) ,, x le 0):} . Investigat...

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  15. Find the number of critical points of the function f (x) = - (3)/(4...

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  16. Find the number of critical points of the function f(x) = |x - 2| +...

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  17. Find the number of critical points of the function f (x) = min (tan...

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  18. Let f (x) = x^(2) , x in [-1 , 2) Then show that f(x) has exactly one ...

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  19. Let f (x) = x + sqrtx . Find the greatest and least value of f(x) for ...

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  20. Let f(x) ={underset(x^(2) +nb " " x ge1)(3-x " "0le x lt1). Find ...

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