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Find the values of a for which the function `f(x)=(a+2)x^3-3a x^2+9a x-a` decreasing for all real values of `xdot`

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To find the values of \( a \) for which the function \[ f(x) = (a+2)x^3 - 3ax^2 + 9ax - a \] is decreasing for all real values of \( x \), we need to analyze the first derivative of the function. ...
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RD SHARMA-INCREASING AND DECREASING FUNCTION -Solved Examples And Exercises
  1. Show that f(x)=cos(2x+pi/4) is an increasing function on (3pi//8,7pi/...

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  2. Show that for a >=1,f(x)=sqrt(3)sinx-cosx-2a x+b is decreasing on Rdot

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  3. Find the values of a for which the function f(x)=(a+2)x^3-3a x^2+9a x-...

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  4. If a , b , c are real numbers, then find the intervals in which f(x)=|...

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  5. Find the intervals in which f(x)=(x-1)^3(x-2)^2 is increasing or decre...

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  6. Find the intervals in which f(x)=(4x^2+1)/x is increasing or decreasin...

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  7. Determine the intervals in which the function f(x)=x^4-8x^3+22 x^2-24 ...

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  8. Find the intervals for which f(x)=x^4-2x^2 increasing or decreasing.

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  9. Determine the values of x for which f(x)=(x-2)/(x+1)x!=-1 is increasin...

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  10. Find the intervals in which f(x)=x/2+2/x , x!=0 is increasing or decre...

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  11. For which values of x , the function f(x)=x/(x^2+1) is increasing and ...

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  12. Find the intervals in which f(x)=(4x^2+1)/x is increasing or decreasi...

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  13. Separate the interval [0,pi/2] into sub intervals in which function f(...

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  14. Show that the function f given by f(x)=tan^(-1)(sinx+cosx), x" ">" "0 ...

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  15. Prove that the function f(x)=tanx-4x is strictly decreasing on (-pi//3...

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  16. Solve: 4x^3-24 x^2+44 x-24 >0 .

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  17. Solve: 1/(x+1)-4/((2+x)^2)>0,\ \ x!=-1,\ -2 .

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  18. Solve: (1+x^2)/(x^2-5x-6)<0

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  19. Sol v e(8x^2+16 x-51)/(2x^2+5x-12)>3

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  20. Solve: (x^2-2x+5)/(3x^2-2x-5)>1/2 .

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