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Show that the function f given by f(x)=x...

Show that the function f given by `f(x)=x^3-3x^2+4x ,x in R`is strictly increasing on R.

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We have given that
`f(x)=x^3-3x^2+4x`
`f'(x)=3x^2-6x+4`
`f'(x)=3(x^2-2x+1)+1`
`f'(x)=3(x-1)^2+1`
For function to be increasing function `f′(x)` must be >`0`
`3(x-1)^2+1`>`0`for all `x in R`
...
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RD SHARMA-INCREASING AND DECREASING FUNCTION -Solved Examples And Exercises
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  3. Show that the function f given by f(x)=x^3-3x^2+4x ,x in Ris strictl...

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

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

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

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

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

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