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Let f be a function defined on [a, b] su...

Let f be a function defined on [a, b] such that `f^(prime)(x)>0`, for all `x in (a ,b)`. Then prove that f is an increasing function on (a, b).

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The correct Answer is:
`rArr f(x_(1)) lt f_(x_(2))" if "x_(1) lt x_(2)`
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MODERN PUBLICATION-APPLICATIONS OF DERIVATIVES-Misellaneous Exercise on Chapter (6)
  1. Show that the normal at any point theta to the curve x=acostheta+at...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. The line y = m x + 1is a tangent to the curve y^2=4xif the value of m...

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  18. The normal at the point (1,1) on the curve 2y+x^2=3is(A) x + y = 0 (B)...

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  19. The normal to the curve x^(2)=4y passing (1, 2) is :

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  20. The points on the curve 9y^2=x^3, where the normal to the curve makes ...

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