A Particle Starts at the Origin and Moves Along the Parabola

question 82

Short Answer

A particle starts at the origin and moves along the parabola $y = x ^ { 2 }$ such that its distance from the origin increases at 4 units per second. How fast is its x-coordinate changing as it passes through the point $( 1,1 )$ ?

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Definitions:

Marginal Revenue

The uplift in revenue achieved by marketing an additional unit of a product or service.

Marginal Cost

The cost incurred by producing one additional unit of a product, a key concept in economic decision-making regarding production levels.

Short-Run Supply Curve

A graphical representation that shows the quantity of goods a firm is willing and able to produce and sell at different price levels over a short period, not allowing for all factors of production to vary.

MC Curve

The Marginal Cost curve, which shows the increase in total cost that arises from producing one more unit of a good or service.