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Prove that f(x)=((1)/(x))^(x) has local ...

Prove that `f(x)=((1)/(x))^(x)` has local maximum at `x=(1)/(e ).x in R^(+)`

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KUMAR PRAKASHAN-APPLICATION OF DERIVATIVES -PRACTICE WORK
  1. What is the maximum slope of the curve y=-x^(3)+3x^(2)+2x-27 ? Also fi...

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  2. Find the co-ordinates of a point on the parabola y=x^(2)+7x+2 which is...

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  3. The total area of a page is 150 square inchese. The combined width of ...

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  4. The three sides of a trapezium are equal, each being 6 cm long. Find t...

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  5. In a right angle triangle, the sum of hypotenuous and one side is give...

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  6. Show that a triangle of maximum area that can be inscribed in a circle...

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  7. The circle x^(2)+y^(2)=1 cats the X - axis at P and Q. Another circle ...

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  8. Two roads OA and OB intersect at an angle 60^(@). A car driver approac...

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  9. Find the interval in which the function f(x)=x^(4)+32x is increasing o...

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  10. Show that the curves xy=a^(2) and x^(2)+y^(2)=2a^(2) touch each other.

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  11. Prove that the slope of tangent at any point of the curve y=6x?^(3)+15...

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  12. Prove that f(x)=((1)/(x))^(x) has local maximum at x=(1)/(e ).x in R^(...

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  13. For simple pendulum, T = 2pi sqrt((l)/(g)) where T is the periodic tim...

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  14. Find the equation of normal to the curve x^((2)/(3))+y^((2)/(3))=a^((2...

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  15. Prove that the function f(x)=2|x-1|+3|x-4| is decreasing in the intrer...

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  16. The radius of the cone is increasing at the rate of 4 cm/se. Its heigh...

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  17. Prove that in all rectangles with given area, the perimeter of square ...

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  18. The equation of a particle in motion is S=(1)/(4)t^(4)-2t^(3)+4t^(2)-7...

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  19. At which point the curve y=-x^(3)+3x^(2)+2x-27 has maximum slope ? How...

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  20. Water comes out from a conical funnel at the rate of 5 cm^(3)//s. When...

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