Consider the function $\displaystyle {f{{\left({x}\right)}}}={2}{x}^{{3}}-{6}{x}$ on the interval $\displaystyle {\left[-{3},{3}\right]}$. Find the average or mean slope of the function on this interval. Preview Question 6 Part 1 of 3  

By the Mean Value Theorem, we know there exists at least one $\displaystyle {c}$ in the open interval $\displaystyle {\left(-{3},{3}\right)}$ such that $\displaystyle {f}'{\left({c}\right)}$ is equal to this mean slope.
For this problem, there are two values of $\displaystyle {c}$ that work.

The smaller one is Preview Question 6 Part 2 of 3  
and the larger one is Preview Question 6 Part 3 of 3