Is what I did correct to determine the relationship between this point and given function?

[itsrayex]

Options are:
A. stationary point
B. maximum point
C. minimum point
D. oblique tangent


I would say A is the correct answer (stationary point) by exclusion. Are the steps I took correct? I am not sure especially regarding finding mins and max.

 

[Dr.Peterson]

Options are:
A. stationary point
B. maximum point
C. minimum point
D. oblique tangent
View attachment 31077

I would say A is the correct answer (stationary point) by exclusion. Are the steps I took correct? I am not sure especially regarding finding mins and max.

Your work and answer are correct; some of the work is redundant, as you already know from the diagram that the derivative is positive everywhere but at x=-1, where is it zero. That shows that it is not a max or a min, and has a horizontal, not oblique, tangent, so it is a stationary point.

You also didn't really need the quadratic formula, as the derivative factors as [imath]e^x(x+1)^2[/imath]. And you didn't have to find the equation of the tangent line; knowing its slope is enough for the question (as I understand it -- it would be helpful if you stated the entire problem exactly, rather than giving it to us in pieces).