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Find the set of values of ' b ' for whic...

Find the set of values of `' b '` for which `f(x)=b(x+cosx)+4` is decreasing on `R` .

Text Solution

Verified by Experts

We have given
`f(x)=b(x+cosx)+4`
Then,
`f'(x)=b(1−sinx)`
Then for decreasing function
`f'(x)<=0`
`b(1−sinx)<=0`for all`x in R`
As, `sinx<=1` for all`x in R`
...
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RD SHARMA-INCREASING AND DECREASING FUNCTION -Solved Examples And Exercises
  1. Find ' a ' for which f(x)=a\ (x+sinx)+a is increasing on R .

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  2. Find the values of ' a ' for which the function f(x)=sinx-a x+4 is inc...

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  3. Find the set of values of ' b ' for which f(x)=b(x+cosx)+4 is decreasi...

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  4. Find the set of values of ' a ' for which f(x)=x+cosx+a x+b is increas...

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  5. Write the set of values of k for which f(x)=k x-sinx is increasing on ...

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  6. If g(x) is a decreasing function on R and f(x)=tan^(-1){g(x)} . State ...

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  7. Write the set of values of a for which the function f(x)=a x+b is decr...

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  8. Write the interval in which f(x)=sinx+cosx ,\ \ x in [0,\ pi//2] is in...

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  9. State whether f(x)=tanx-x is increasing or decreasing its domain.

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  10. Write the set of values of a for which f(x)=cosx+a^2\ x+b is strictly ...

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  12. The function f(x)=cot^(-1)x+x increases in the interval (a) (1,\ oo) ...

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  13. The function f(x)=x^x decreases on the interval (a) (0,\ e) (b) (0,\ ...

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  14. The function f(x)=2log(x-2)-x^2+4x+1 increases on the interval (a) (1,...

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  15. If the function f(x)=2x^2-k x+5 is increasing on [1,\ 2] , then k lies...

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  16. IF f(x)=x^3+a x^2+b x+5sin^2x\ is a strictly increasing functio...

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  18. If the function f(x)=2tanx+(2a+1)(log)e|secx|+(a-2)x is increasing on ...

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  19. Let f(x)=tan^(-1)(g(x)) , where g(x) is monotonically increasing for 0...

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