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Show that for a >=1,f(x)=sqrt(3)sinx-cos...

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

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given `f(x)= sqrt(3) sinx-cosx-2ax+b`
`a>=1`
now,`f^'(x)=sqrt3 cosx+sinx-2a`
`2[(sqrt3)/2 cosx +1/2sinx]-2a`
...
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RD SHARMA-INCREASING AND DECREASING FUNCTION -Solved Examples And Exercises
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  2. Show that f(x)=cos(2x+pi/4) is an increasing function on (3pi//8,7pi/...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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