Answer
See graph and explanations.
Work Step by Step
Step 1. Draw two functions ($f(x)$ and $g(x)$) as shown in the figure. They have two intersection points where $f(a)=g(a)$ and $f(b)=g(b)$ ($a\lt b$).
Step 2. We need to find a point $c$ between $a$ and $b$ such that $f'(c)=g'(c)$ or $f'(c)-g'(c)=0$
Step 3. Consider the difference of the two functions $h(x)=f(x)-g(x)$; we have $h(a)=h(b)=0$. Based on Rolle's Theorem, there must be a point $c$ in $(a,b)$ such that $h'(c)=0$. Thus, we have $f'(c)-g'(c)=0$ or $f'(c)=g'(c)$, indicating two parallel or identical tangent lines.
