These can be quite tricky.
consider the first one.
when x=1/6 the gradient is 0
when x=-3/2 the gradient is 0.
plot those 2 points first.
now when x>1/6 the gradient is negative and it is getting steeper and steeper.
so as x tends to infinity, the gradient tends to -infinity.
When x is <-2/3 the same thing is happening
so as x tends to -infinity, the gradient tends to -infinity also.
Now between -2/3 and 1/6 the curve is increasing. I mean the gradient of the tangent is positive
Somewhere in the middle between the 2 is a point of inflection. This is where the first derivative is still positive but it is becoming smaller so the graphe between -2/3 and 1/6 will look a bit like a concave down parabola. the point at the top will be the point of inflection of the original function graph.
Do you get all that? Try drawing it. I think these are fun to work out.
Then have a go at the second one.
Partial mathematician:
I know you are keen to learn and I really do appreciate that, I want you to stick around for a long time .... but please stop pretending that you know a whole lot more than you really do. You leave people confused and sometimes annoyed. Some of your input is really good, I know this, but .... you can finish this sentence for yourself.
