Consider the function $\displaystyle {f{{\left({x}\right)}}}={3}{x}^{{3}}-{5}{x}$ on the closed interval $\displaystyle {\left[{2},{4}\right]}$.

Find the exact value of the slope of the secant line connecting $\displaystyle {\left({2},{f{{\left({2}\right)}}}\right)}$ and $\displaystyle {\left({4},{f{{\left({4}\right)}}}\right)}$.

$\displaystyle {m}=$ Preview Question 6 Part 1 of 2  

By the Mean Value Theorem, there exists $\displaystyle {c}$ in $\displaystyle {\left({2},{4}\right)}$ so that $\displaystyle {m}={f}'{\left({c}\right)}$. Find all values of such $\displaystyle {c}$ in $\displaystyle {\left({2},{4}\right)}$. Enter exact values. If there is more than one solution, separate them by a comma.

$\displaystyle {c}=$ Preview Question 6 Part 2 of 2