# some graphing help

• June 25th 2006, 03:21 AM
kwtolley
algebra and trigonometry with analytic geometry problem
If f(x)=x(x-1)(x-4)^2, use interval notation to give all values of x where f(x)>0. My answer is (0,1) u (4,infy), thanks for looking it over with me.
• June 25th 2006, 03:43 AM
CaptainBlack
Quote:

Originally Posted by kwtolley
If f(x)=x(x-1)(x-4)^2, use interval notation to give all values of x where f(x)>0. My answer is (0,1) u (4,infy), thanks for looking it over with me.

$f(x) \to +\infty$ as $x \to \pm \infty$, and its roots are $0,1,4$, with the last having a multiplicity of 2 (and so the function just touches the x-axis at $x=4$. So $f(x)>0$ in:

$(-\infty,0) \cup (1,4) \cup (4,\infty)$

RonL
• June 25th 2006, 03:47 AM
kwtolley