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Show that the function given by f(x)=(lo...

Show that the function given by `f(x)=(logx)/x`has maximum at `x = e`.

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MODERN PUBLICATION-APPLICATIONS OF DERIVATIVES-Misellaneous Exercise on Chapter (6)
  1. Using differentials, find the approximate value of each of the followi...

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  2. Using differentials, find the approximate value of (33)^(1//5)

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  3. Show that the function given by f(x)=(logx)/xhas maximum at x = e.

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  4. The two equal sides of an isosceles triangle with fixed base b are ...

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  5. Find the equation of the normal to curve y^(2)=4x at the point (1, 2).

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  6. Show that the normal at any point theta to the curve x=acostheta+at...

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  7. Find the intervals in which the function f given by f(x)=(4sinx-2x-x c...

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  8. Find the intervals in which the function f given by f(x)=x^3+1/(x^3), ...

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  9. Find the maximum are of the isosceles triangle inscribed in the ell...

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  10. A tank with rectangular base and rectangular sides, open at the top...

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  11. The sum of the perimeter of a circle and square is k, where k is so...

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  12. A window is in the form of a rectangle surmounted by a semicircular...

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  13. A point on the hypotenuse of a triangle is at distance a and b from t...

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  14. Find the points at which the function f given by f(x)=(x-2)^4(x+1)^3 h...

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

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  16. Show that the altitude of the right circular cone of maximum volume...

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  17. Let f be a function defined on [a, b] such that f^(prime)(x)>0, for al...

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  18. Show that the height of the cylinder of maximum volume that can be ...

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  19. Show that height of the cylinder of greatest volume which can be insc...

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  20. A cylindrical tank of radius 10 m is being filled with wheat at the r...

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