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

question 56

Multiple Choice

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

• A) \(c = 1\)
• B) \(c = 5\)
• C) \(c = - 2\)
• D) \(c = - 5\)
• E) \(c = 2\)

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Definitions:

Value of the Marginal Product

The additional revenue generated by employing one more unit of a factor, holding all else constant.

Marginal Product

The additional output that is produced by adding one more unit of a specific input, while holding other inputs constant.

Price Per Unit

The cost of a single unit of a product, often used to compare different product costs directly.

Moisture Farm

A fictional type of farm found in science fiction, particularly in the Star Wars universe, designed for the collection and harvesting of water from the atmosphere.