Re-writing f as
should hopefully convince you that for real x this is always positive.
I am attempting to graph .
My textbook shows the graph as being defined between and in fact the derivative indicates that the graph has a local maximum at . In my textbook the graph is convex and positive between
The problem is that is approximately . Which means it's negative, unless I am calculating incorrectly? What has me really confused is that MuPAD does not show the graph as defined between and which has got me thinking the textbook might be wrong. When calculating do you square the minus three and then take a cube root? Maybe that's what's wrong. Maybe f(0) is actually positive?