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Question

Prove that the function given by f(x)=x33x2+3x10 is increasing in R.


Solution

Given, f(x)=x33x2+3x100
f(x)=3x26x+3=3(x22x+1)=3(x1)2
For any xϵR,(x1)2>0 since, a perfect square cannot be negative
Then, f(x)>0. Hence, the given function f is an increasing function on R.

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