For What Value of the Constant $c$ Is the Function $f$ Continuous On

question 60

Short Answer

For what value of the constant $c$ is the function $f$ continuous on $( - \infty , \infty )$ ?
$$f ( x ) = \left\{ \begin{array} { l l l } c x + 5 & \text { for } & x \leq 2 \\c x ^ { 2 } - 5 & \text { for } & x > 2\end{array} \right.$$

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Definitions:

Variable Selling

Costs that vary directly with the level of sales activity, such as commissions or credit card fees.

Special Order

A customer order for goods or services that is outside a company's normal production or service offerings, often requiring unique specifications or quantities.

Financial Advantage

A benefit or edge gained in financial terms, often through investments, cost savings, or favorable financial conditions.

Joint Process

A manufacturing operation that simultaneously produces more than one product from a single raw material input.