Determine If the Piecewise Defined Function Is Differentiable at the Origin

question 178

Multiple Choice

Determine if the piecewise defined function is differentiable at the origin.
- $$g ( x ) = \left\{ \begin{array} { l l l } x ^ { 7 / 8 } & \text { if } x \geq 0 & \\x ^ { 1 / 8 } & & \text { if } x < 0\end{array} \right.$$

• A) Differentiable
• B) Not differentiable

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Definitions:

Satisfaction

The fulfillment or gratification of a need, desire, or appetite, often used in the context of consumer experiences with goods or services.

Demand Curve

A visual depiction showing how the quantity of a product demanded by buyers varies with its price.

Horizontal Summation

A method used to determine the total market demand or supply by adding together the quantities demanded or supplied at each price by all individuals.

Substitution Effect

The change in consumption patterns due to a change in the relative prices of goods.