
Open Intervals
I plugged in the equation x^42x^3+5x+4 into my calculator. I'm looking at the graph, but I can't find the points of inflection.
The problem is f(x)=x^42x^3+5x+4 and I must find the intervals in which f is concave up (down), Then I have to determine the xcoordinates of all inflection points of f.
So far I know that one of the concave down intervals is (0,infinity)
The method I used to get that cannot be used for the others so I'm here to ask for help on how to do this right.

Solving for $\displaystyle f''(x)=0$ will give you the values of $\displaystyle x$ at which $\displaystyle f(x)$ has points of inflection. Indeed, $\displaystyle f''(x)=12x(x+1)=0$ when $\displaystyle x=1,\,0.$ So you should investigate the behaviour of $\displaystyle f(x)$ in the three separate intervals $\displaystyle (\infty,\,1),\ (1,\,0),\ (0,\,\infty).$

Thank you, I was missing going to the second derivative. Thanks.