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Find the minimum value of the function x...

Find the minimum value of the function `x^(x)`.

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To find the minimum value of the function \( f(x) = x^x \), we will follow these steps: ### Step 1: Rewrite the function Let \( y = x^x \). ### Step 2: Take the natural logarithm Taking the natural logarithm of both sides, we have: \[ ...
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NAGEEN PRAKASHAN ENGLISH-APPLICATIONS OF DERIVATIVES-Miscellaneous Exercise
  1. Find the minimum value of the function x^(x).

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  2. Using differentials, find the approximate value of each of the follow...

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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 the curve x^2=4\ y which passes ...

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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 area of the greatest isosceles triangle that can be inscri...

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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...

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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 in...

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

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  21. The slope of the tangent to the curve x=t^2+3t-8,y=2t^2-2t-5at the po...

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