#curve sketching
9 messages · Page 1 of 1 (latest)
The highlighted yellow part means that the derivative at the critical points where x= 3 and 1 is 0 i.e a horizontal tangent line.
I don't understand what you've written up above, but that last person where you say its concave downwards and upwards at the same at x = -1 is wrong.
When the sign of concavity changes we have an inflection point that is f''(-1) = 0. Where the change in the instantaneous rate of change is 0, roughly remains the same for like a split second.