Provide an Appropriate Response
-Let $\mathrm { p } _ { 0 } , \mathrm { p } _ { 1 }$

question 25

Multiple Choice

Provide an appropriate response
-Let $\mathrm { p } _ { 0 } , \mathrm { p } _ { 1 }$ , and $\mathrm { p } _ { 2 }$ be points in $\mathfrak { R } ^ { \mathrm { n } }$ and define $\mathrm { f } _ { 0 } ( \mathrm { t } ) = ( 1 - \mathrm { t } ) \mathrm { p } _ { 0 } + \mathrm { tp } _ { 1 } , \mathrm { f } _ { 1 } ( \mathrm { t } ) = ( 1 - \mathrm { t } ) \mathrm { p } _ { 1 } + \mathrm { tp } _ { 2 }$ , and $g ( t ) = ( 1 - t ) f _ { 0 } ( t ) + t f _ { 1 } ( t )$ for $0 \leq t \leq 1$ .
Find $\left. g \frac { 1 } { 2 } \right)$ in terms of the three points.

• A) \(g \left( \frac { 1 } { 2 } \right) = \frac { 3 } { 2 } p _ { 0 } + \frac { 1 } { 2 } p _ { 1 } - \frac { 1 } { 2 } p _ { 2 }\)
• B) \(g \left( \frac { 1 } { 2 } \right) = \frac { 1 } { 2 } \mathrm { p } _ { 0 } + \frac { 1 } { 2 } \mathrm { p } _ { 1 }\)
• C) \(g \left( \frac { 1 } { 2 } \right) = \frac { 1 } { 4 } p _ { 0 } + \frac { 1 } { 2 } p _ { 1 } + \frac { 1 } { 4 } p _ { 2 }\)
• D) \(g \left( \frac { 1 } { 2 } \right) = \frac { 9 } { 16 } \mathrm { p } _ { 0 } + \frac { 3 } { 8 } \mathrm { p } _ { 1 } + \frac { 1 } { 16 } \mathrm { p } _ { 2 }\)

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Definitions:

Midpoint Method

is a technique in economics used to calculate the elasticity of demand or supply, providing a more accurate measure by averaging the starting and ending points.

Elasticity of Demand

A measure of how sensitive the demand for a good or service is to changes in its price.

Quantity Demanded

The complete amount of a product or service that purchasers have the willingness and capacity to obtain at a set price.

Price Inelastic

A situation where the quantity demanded or supplied of a good is not significantly affected by changes in price.