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Let g(x)=(f(x))^3-3(f(x))^2+4f(x)+5x+3si...

Let `g(x)=(f(x))^3-3(f(x))^2+4f(x)+5x+3sinx+4cosxAAx in Rdot` Then prove that `g` is increasing whenever is increasing.

Text Solution

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`g(x)=f(x)^(3)-3f(x)^(2)+4f(x)+5x+3sinx+4cosx`
`g(x)3f(x)^(2)-6f(x)+4f(x)+5+3cosx-4sinx`
Now `3f(x)^(2)-6f(x)+4=3f(x)-1^(2)+1lgt0`
and -5 `le3cos x-4sin x le5`
`therefore 0ge3cos x -4sind x+5 le10`
When f(x) increases f(x) `ge0`
So from `(1),g(x)ge0`
So ,g(x) in increasing whenever f(x) increases.
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