Question

are of change foeleey is beHer noun as acceleration When our function f(x) has a context, such as representing population over time or cost to produce x items, the derivative will have a context as well. To understand the derivative we must look at it not just algebraically and graphically, but also in words. In the following scenarios, explain what the derivative of the given function would tell us. Be sure to include units where appropriate. Where do you think the derivative will be greatest or smallest? Cx) is the cost of producing x ounces of gold from a gold mine. P(x) is the profit of a t-shirt company after selling x t-shirts. P(t) is the population of deer on an island at t years after 1990. H(t) is the temperature in Tucson t days after January 1", 2018. V(t) is the volume of water in a tank that is being filled by a hose after t minutes.

Answer 1

The derivative of C(x), that is C'(x) would represent the rate of change in the cost of production with respect to change in the quantity 'x' of gold produced (in ounces). In more simpler terms, C'(x) would represent cost of production of every ounce of gold at any stage after production of 'x' number of ounces of gold.

The derivative of P(x), that is P'(x) would represent the rate of change in the profit with respect of change in the number 'x' of t-shirts sold. In more simpler terms P'(x) would represent profit on selling every t-shirt at any stage after sale of 'x' number of t-shirts.

The derivative of P(t), that is P'(t) would represent the rate of change in the population of dears per year after 't' years from 1990.

The derivative of H(t), that is H'(t) would represent the rate of change in temperature per day at Tuscan, 't' number of days after 1st Jan 2018.

The derivative of V(t), that is V'(t) would represent the rate at which the volume of water in the tank is increasing per minute, 't' number of minutes after the tank started filling.

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