Quiz about Application Of Derivatives

Question 1

The function $${D}$$ gives the day length, in minutes, of the $$n^{	ext {th }}$$ day of the year in Juneau, Alaska. What is the best interpretation for the following statement $${D}^{\prime}(10)=3$$

Accepted Answer

Covalent bond

Answer

On January 10, the day length is increasing at a rate of 3 minutes per day.

Answer

On January 10 , the day is 3 minutes long.

Answer

On January 10, the day length is increasing at a rate of 3 days per minute.

Answer

Until January 10, the day length is increasing at a rate of 3 minutes per day.

Question 2

The function $${C}$$ gives the costs (in dollars) of producing $${x}$$ liters of a certain sauce.What is the best interpretation for the following statement?

The slope of the line tangent to the graph of $$C$$ at $$x=12$$ is equal to 4 .

Accepted Answer

Covalent bond

Answer

When the amount of sauce produced is 12 liters, the costs increase at a rate of 4 dollars per liter

Answer

At the time when 12 liters of sauce are produced, the costs increase by 4 dollars.

Answer

The costs of producing the sauce increase at a rate of 44 dollars per 12 liters.

Answer

It costs 4 dollars to produce 12 liters of the sauce.

Question 3

P gives the lion population at a certain game reserve $$t$$ years after the reserve was established. What is the best interpretation for the following statement?

The value of the derivative of $${P}$$ at $${t}=6$$ is equal to $$12$$ .

Accepted Answer

Covalent bond

Answer

After 6 years, the lion population grows at a rate of 12 lions per year.

Answer

After 6 years, the lion population grows at a rate of 12 lions.

Answer

The lion population grows at a rate of 12 lions per 6 years.

Answer

After 6 years, there were 12 lion is in th reserve

Question 4

$$P$$ gives the population of a town $$t$$ years after it was founded. What is the best interpretation for the following statement?

The slope of the line tangent to the graph of $$P$$ at $$t=2$$ is equal to $$-10$$.

Accepted Answer

Covalent bond

Answer

After 2 years, the town's population decreased at a rate of 10 people per year.

Answer

Over the first two years, the town's population decreased by 10 people per year.

Answer

After 2 years, the rate of change of the population decreased at a rate of 10 people per year.

Answer

After 2 years, the town's population decreased at a rate of 10 people.

Question 5

An object is moving along a line. The following graph gives the object's velocity over time. For the point $$({9}, 3)$$ on the graph, is the object moving forward, backward, or neither?

![](http://admin.getprephub.com/media/editor/aod5_20221017222510851095.png)

Accepted Answer

Covalent bond

Answer

Moving forward

Answer

Moving backward

Answer

Neither

Answer

Not possible to determine

Application Of Derivatives Calculus Maths Problems and Solutions

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