Find the Slope of the Curve at the Indicated Point $v$

question 4

Multiple Choice

Find the slope of the curve at the indicated point.
-For a motorcycle traveling at speed $v$ (in $m p h$ ) when the brakes are applied, the distance $d$ (in feet) required to stop the motorcycle may be approximated by the formula $\mathrm { d } = 0.05 \mathrm { v } ^ { 2 } + \mathrm { v }$ . Find the instantaneous rate of change of distance with respect to velocity when the speed is $46 \mathrm { mph }$ .

• A) 5.6 mph
• B) 47 mph
• C) 11.2 mph
• D) 4.6 mph

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Definitions:

Acres of Pasture

Measures of land area dedicated to grazing livestock or used for fodder production.

Budget

An estimate of income and expenditure for a set period of time.

Cost Function

A relationship in mathematics that outlines how changes in production volume affect the costs associated with production.

Long-run Equilibrium

A state where all factors of production and outputs are variable, and economic agents have fully adjusted to any changes, leading to no further tendency for change.