Science:Math Exam Resources/Courses/MATH110/April 2019/Question 06/Statement

Consider a function $g(x)$ that is continuous and differentiable everywhere. Assume that $g(x)$ has ALL of the following properties:

• $\underset{x\to \mathrm{\infty }}{\lim }g(x)=-\mathrm{\infty }$ and $\underset{x\to -\mathrm{\infty }}{\lim }g(x)=0$;

• $g^{\prime }(x)>0$ for $x<0$ and $g^{\prime }(x)<0$ for $x>0$;

• $g^{″}(x)>0$ for $x<-1$ and $g^{″}(x)<0$ for $x>-1$.

Sketch the graph of $y=g(x)$ and indicate where the inflection point(s) occur.