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Prove that the function given by f(x) = ...

Prove that the function given by f(x) = cos x is
(a) decreasing in (0, `pi` )
(b) increasing in `(pi, 2pi)`, and
(c) neither increasing nor decreasing in (0, `2pi)`.

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NCERT BANGLISH-APPLICATION OF DERIVATIVES-EXERCISE 6.6
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  2. Using differentials, find the approximate value of each of the followi...

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

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  6. Show that the normal at any point θ to the curve x = a costheta + a th...

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

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

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  9. Find the maximum area of an isosceles triangle inscribed in the ellips...

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

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

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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 th...

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

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

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

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  17. Let f be a function defined on [a, b] such that f ′(x) gt 0, for all x...

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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 ra...

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

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