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Prove that the function f(x)=3x^5+40 x^3...

Prove that the function `f(x)=3x^5+40 x^3+240 x` is increasing on `R` .

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We have given
`f(x)=3x^5+40 x^3+240 x`
Differentiation w.r.t `x`
`f(x)=15x^4+120x^2+240 `
for the fucntion to be increasing `f′(x)` must be greater than zero
`15x^4+120x^2+240`>`0 `
`3x^4+24x^2+48`>`0 `
...
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RD SHARMA-INCREASING AND DECREASING FUNCTION -Solved Examples And Exercises
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  2. Prove that the function f given by f(x)=x-[x] is increasing in (0,\ 1)...

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  3. Prove that the function f(x)=3x^5+40 x^3+240 x is increasing on R .

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  4. Prove that the function f given by f(x)=logcosx is strictly increasing...

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  6. Prove that the function f(x)=cosx is strictly decreasing in (0,\ pi)

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  7. Prove that the function f(x)=cosx is strictly increasing in (pi,\ 2pi)

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  8. Prove that the function f(x)=cosx is neither increasing nor decreas...

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  13. Let f defined on [0, 1] be twice differentiable such that | f"(x)| ...

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  16. Find the intervals in which f(x)=s in\ x(1+cosx),\ \ 0<x<pi/2 is incre...

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  17. What are the values of ' a ' for which f(x)=a^x is increasing on R

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  18. What are the values of ' a ' for which f(x)=a^x is decreasing on R

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  19. Write the set of values of ' a ' for which f(x)=(log)a x is increasing...

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  20. Write the set of values of ' a ' for which f(x)=(log)a x is decreasing...

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