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Test whether the following funtions are ...

Test whether the following funtions are increasing or decreasing :
`f(x)=2-3x+3x^(2)-x^(3), x in R`.

Text Solution

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The correct Answer is:
decreasing for all `x in R`, when `x ne 1`.
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NAVNEET PUBLICATION - MAHARASHTRA BOARD-APPLICATIONS OF DERIVATIVES -Examples for Practice
  1. Verify Rolle's theorem for each of the following functions : f(x) = ...

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  2. Test whether the following funtions are increasing or decreasing : f...

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  3. Test whether the following funtions are increasing or decreasing : f...

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  4. Find the values of x such that f(x)=x^(3)+12x^(2)+36x+6 is an increasi...

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  5. Find the values of x such that f(x)=2x^(3)-9x^(2)+12x+2 is a decreasin...

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  6. Find the values of x if f(x)=(x)/(x^(2)+1) is an increasing function

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  7. Find the values of x if f(x)=(x)/(x^(2)+1) is a decreasing function.

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  8. Examine the following functions for maxima and minima : f(x)=2x^(3)-...

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  9. Examine the following functions for maxima and minima : f(x)=x^(2)+(...

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  10. Examine the following functions for maxima and minima : f(x)=3x^(3)-...

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  11. Examine the following functions for maxima and minima : f(x)=x^(2)e^...

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  12. Examine the following functions for maxima and minima : Show that f(...

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  13. Examine the following functions for maxima and minima : Find the max...

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  16. If x+y=8, then show that the maximum value of x^(2)y is (2048)/(27).

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