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Find the values of `k` for which `f(x)=k x^3-9k x^2+9x+3` is increasing on `R` .

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To find the values of \( k \) for which the function \[ f(x) = kx^3 - 9kx^2 + 9x + 3 \] is increasing on \( \mathbb{R} \), we need to analyze the first derivative of the function. ...
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RD SHARMA-INCREASING AND DECREASING FUNCTION -Solved Examples And Exercises
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  7. Find the intervals in which f(x)=2x^3-12 x^2+18 x+15 is increasing or ...

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  9. Find the intervals in which f(x)=8+36 x+3x^2-2x^3 is increasing or dec...

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  10. Find the intervals in which f(x)=5x^3-15 x^2-120 x+3 is increasing or ...

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  11. Find the intervals in which f(x)=x^3-6x^2-36 x+2 is increasing or decr...

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  12. Find the intervals in which f(x)=2x^3-15 x^2+36 x+1 is increasing or d...

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  13. Find the intervals in which f(x)=2x^3+9x^2+12 x+20 is increasing or de...

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  14. Find the intervals in which f(x)=2x^3-9x^2+12 x-5 is increasing or dec...

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  15. Find the intervals in which f(x)=6+12 x+3x^2-2x^3 is increasing or dec...

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  16. Find the intervals in which f(x)=2x^3-24 x+107 is increasing or decrea...

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  17. Find the intervals in which f(x)=-2x^3-9x^2-12 x+1 is increasing or de...

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  18. Find the intervals in which f(x)=(x-1)(x-2)^2 is increasing or decreas...

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  19. Find the intervals in which f(x)=x^3-12 x^2+36 x+17 is increasing or d...

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  20. Find the intervals in which f(x)=2x^3-24 x+7 is increasing or decreasi...

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