Quiz about Application Of Derivatives

Question 1

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 2

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 3

The differentiable functions $${X}$$ and $${y}$$ are related by the following equation:

Also, $$\frac{d x}{d t}=4$$. Find $$\frac{d y}{d t}$$ when $${y}=-2$$

$$y^{3}-3 y^{2}=11-2 x$$

Accepted Answer

Covalent bond

Answer

$$-\frac{1}{3}$$

Answer

$$-\frac{1}{2}$$

Answer

$$-\frac{1}{4}$$

Answer

$$\frac{1}{3}$$

Question 4

Anatoli was given this problem:

Two cars are driving towards an intersection from perpendicular directions. The first car's velocity is 2 meters per second and the second car's velocity is 9 meters per second. At a certain instant $$t_0$$, the first car is a distance $${x}(t_0)$$ of 8 meters from the intersection and the second car is a distance $$y(t_0)$$ of 6 meters from the intersection. What is the rate of change of the distance $$d(t)$$ between the cars at that instant?

Accepted Answer

Covalent bond

Answer

$$[d(t)]^2=[x(t)]^2+[y(t)]^2$$

Answer

$$d(t)=\frac{x(t)+y(t)}{2}$$

Answer

$$d(t)=\sqrt{x(t) y(t)}$$

Answer

None of the above

Question 5

Consider the following problem:

The length $${m}({t})$$ of a rhombus's diagonal is decreasing at a rate of $$3 {~cm} / {h}$$ and the length $${n}({t})$$ of the other diagonal is increasing at a rate of $$11 {~cm} / {h}$$. At a certain instant $$t_{0}$$, the decreasing diagonal is $$5 {~cm}$$ and the increasing diagonal is $$5 {~cm}$$. Using the given data find the rate of change of the area $${A}({t})$$ of the rhombus at that instant?

Accepted Answer

Covalent bond

Answer

Data is not given

Answer

$$11$$

Answer

$$-5$$

Answer

$$3$$

Application Of Derivatives Calculus Maths Problems and Solutions

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