$92218$

webassign$$net

Step $1$

Recall that a function $f$ is continuous at a number $a$ if the following holds$$

$\underset{xa}{lim}f(x)=f(a)$

We are given the following$$

$f(x)=\{\begin{array}{ccc}c{x}^2+5x& if& x<mn>6</mn>\\ x^3-cx& if& x6\end{array}$

We note that for all values of the constant $c$ the function $f$ is continuous on both $(-,6)$ and $(6,)$The only case that we need to consider is when $x=6$For the function $f$ to be continuous on $(-,)$we need to ensure that there is not a discontinuity at $x=6$To do so$$we must determine the value of $c$ such that the following holds$$

$\underset{x{6}^{-}}{lim}f(x)=\underset{x{6}^{+}}{lim}f(x)$