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Show that , the maximum value of the function `(1)/(3)x^(3)-2x^(2)+3x+1` is `(4)/(3)` more than its minimum value.

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CHHAYA PUBLICATION-MAXIMA AND MINIMA -EXERCISE Short Answer Type Questions
  1. Find for what values of x the following functions are maximum and mini...

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  2. Given f(x)=x^(3)-6x^(2)+9x-8. Find the values of x for which f'(x)=0 ...

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  3. Show that , the maximum value of the function (1)/(3)x^(3)-2x^(2)+3x+1...

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  4. Find the maximum value of sinx +cosx and the value of x for which it i...

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  5. Show that , the function logcos^(2)x+secx is maximum at x=0 and minim...

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  6. Prove that , the minimum value of (i) 4e^(2x)+9e^(-2x)" is "12 , ...

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  7. Show : 4^(x)-8xlog(e)2 is minimum at x=1

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  8. Show : x^(2)"log"(1)/(x) is maximum at x=(1)/(sqrt(e))

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  9. Show : sinx(1+cosx) is maximum at x=(pi)/(3)

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  10. Show : (2theta-sin2theta)/(theta^(2))(thetagt0) is maximum at theta=...

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  11. If (x)/(2)+(y)/(3)=1 , find the minimum value of x^(2)+y^(2).

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  12. If 2x+3y=4 , find the maximum or minimum value of xy.

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  13. Show that , the difference between the maximum and minimum values of ...

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  14. Find the critical points of each of the following functions : sin2...

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  15. Find the critical points of each of the following functions : y=e^(...

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  16. Find the critical points of each of the following functions : f(x)=...

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  17. The perimeter of a rectangle is 100 cm. If the area of the rectangle ...

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  18. Show that , of all rectangles of given permeter , the square has the g...

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  19. Prove that , of all rectangles of given area , the square has the leas...

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  20. Find the dimensions of the rectangle of maximum perimeter that can be ...

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