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:

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

• $g'(x)>0$ for $x<0$ and $g'(x)<0$ 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.