Math Help Forum: Open Intervals

I plugged in the equation -x^4-2x^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^4-2x^3+5x+4 and I must find the intervals in which f is concave up (down), Then I have to determine the x-coordinates 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 will give you the values of at which has points of inflection. Indeed, when So you should investigate the behaviour of in the three separate intervals

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