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If f(x)=10-9x+6x^(2)-x^(3), examine whet...

If `f(x)=10-9x+6x^(2)-x^(3)`, examine whether `f(x)` increases or decreases for values of x, for which
`1 lt x lt 3`.

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The correct Answer is:
`1 lt x lt 3`.
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CHHAYA PUBLICATION-INCREASING AND DECREASING FUNCTION-Illustrative Examples
  1. If f(x)=10-9x+6x^(2)-x^(3), examine whether f(x) increases or decrease...

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  2. If f(x)=10-9x+6x^(2)-x^(3), examine whether f(x) increases or decrease...

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    |

  3. If f(x)=10-9x+6x^(2)-x^(3), examine whether f(x) increases or decrease...

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

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

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  6. Show that, for 0 lt theta lt pi/2, (sin theta)/theta steadily decrease...

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  7. Find the intervals in which the function f given by f(x)=sin x + cos x...

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  8. Find the intervals in which the function f given by f(x)=sin x + cos x...

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  9. Find the intervals in which the function f(x)=x^(x) (x gt 0) is increa...

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  10. Find the intervals in which the function f(x)=x^(x) (x gt 0) is decrea...

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  11. Show that f(x)=tan^(-1)(cos x+sin x) is a stictly increasing function ...

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  12. Prove that the function f(x)=x^(3)-x^(2) is neither increasing nor dec...

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  13. Find the intervals in which the function f(x)=(x+1)^(3)(x-3)^(3) is in...

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  14. Find the intervals in which the function f(x)=(x+1)^(3)(x-3)^(3) is de...

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  15. Sparate the interval [0, pi/2] into sub-intervals in which f(x)=sin^(4...

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  16. Sparate the interval [0, pi/2] into sub-intervals in which f(x)=sin^(4...

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  17. Find the intervals in which the function f(x)=log (1+x) -x/(1+x) is in...

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  18. Find the intervals in which the function f(x)=log (1+x) -x/(1+x) is de...

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  19. If x gt 0, show that, x gt log (1+x) gt x-x^(2)/2.

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  20. Let y=3x.(x+a)/(x+b)+5 [a and b are positive constants and a gt b] be ...

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