Show that $2x^3+2x^2-10x+6$ is positive if $x>1$ 
Show that $2x^3+2x^2-10x+6$ is positive if $x>1$ 

I have tried to solve it using mean value theorem but it doesn't work. Please anyone help me to solve this.

Hint. Let $f(x)=2x^3+2x^2-10x+6$. Trying to use the Mean Value Theorem, you computed the derivative $f'$. Note that $f(1)=f'(1)=0$ which implies that $1$ is a double root of $f$, that is the polynomial $f$ is divisible by $(x-1)^2$. Now you should be able to get the complete factorization of $f$ and to show the given inequality.
