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Prove that the function f given by

Question:

Prove that the function f given by $f(x)=x^{3}-3 x^{2}+4 x$ is strictly increasing on $R$ ?

Solution:

given $f(x)=x^{3}-3 x^{2}+4 x$

$\therefore f(x)=3 x^{2}-6 x+4$

$=3\left(x^{2}-2 x+1\right)+1$

$=3(x-1)^{2}+1>0$ for all $x \in R$

Hence $f(x)$ is strickly increasing on $R$

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