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Find the value of X for which f(X) is ei...

Find the value of X for which f(X) is either a local maximum or a local minimum when `f(X) = X^3-3X^2-9X+6`.

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MODERN PUBLICATION-APPLICATIONS OF DERIVATIVES-PROBLEM
  1. Is f(X)= 20-X-cos X, increasing always? Justify your answer.

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  2. State where y = sin x attains a maximum value in the interval [0,pi].

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  3. Find the value of X for which f(X) is either a local maximum or a loca...

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  4. State where y = sin x attains a maximum value in the interval [0,pi].

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  5. Find the point on the curve, y=2x^2-6x-4 at which the tangent is paral...

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  6. For what values of x,f(x) = x^3-12x is increasing.

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  7. Find the maximum and minimum of f(X) = 3+|X-2| in -2leXle5.

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  8. For what value of k,f(x) = kx^3+3 is decreasing?

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  9. Write the absolute maximum and absolute minimum of the function f(x)=x...

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  10. Find the equation of tangent to the curve x=y^2-2 at the points where ...

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  11. f(x) = x^4-63x^2+ax+9 attains its maximum value at x=1 in the interval...

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  12. Find the points on the curve 9y^2 = x^3 where the normal to the curve ...

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  13. Find the equation of normal to the circle x^2+y^2 = 5 at (2,1).

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  14. Find the intervals where the function f(x)=tanx-4(x-2) is increasing a...

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  15. Show that for f(x) = x+1/x the local maximum is less than local minimu...

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  16. Find the points on the curve 9y^2 = x^3 where the normal to the curve ...

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  17. Find the point (S) on the curve x=(3at)/(1+t^2), y=(3at^2)/(1+t^2) whe...

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  18. Find the equation of the tangent and normal to [x/a]^(1/3)+[y/b]^(1/3)...

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  19. Show that the function e^x/x^p is strictly increasing for x gt p gt 0.

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  20. Show that x/(1+ x tan x,) x in (0,pi/2)is maximum when x = cos x.

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