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.

$f(x)=\{\begin{array}{ccc}{}^2& 5xIf& x<mn>4</mn>\\ x^3-x& if& x4\end{array}$

We note that for all values of the constant $c$ the function $f$ is continuous on both $(-m,4)$ and $(4,).$ The only ca must determine the value of c such that the following holds.

$\underset{x{4}^{-}}{lim}f(x)=\underset{x{4}^{}}{lim}f(x)$

Find the following limits$.$

$\underset{x{4}^{-}}{lim}f(x)=\underset{x{4}^{-}}{lim}(c{x}^{2}5x)$

$=$

$\underset{x{4}^{}}{lim}f(x)=\underset{x{4}^{}}{lim}(x^3-cx)$

$=$