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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.

Text Solution

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`f(x) = x^(2)+ax+1`
` f'(x) = 2x +a`
In the interval (1, 2),
` 1 lt x lt 2`
` rArr 2 lt 2x lt 4`
` rArr 2+ a lt 2x + a lt 4 + a`
` rArr 2+ a lt f'(x) lt 4+ a`
`:' f(x)` is strictly increasing function.
`:. 2+ a gt 0`
` rArr a gt - 2`
` rArr ` Minimum value of a = - 2.
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