Quiz about Application Of Derivatives

Question 1

A man $$1.6 {~m}$$ tall walks at the rate of $$0.3 {~m} / {sec}$$ away from a street light that is $$4 {~m}$$ above the ground. At what rate is the tip of his shadow moving? At what rate is his shadow lengthening?

Accepted Answer

Covalent bond

Answer

$$0.5 {~m} / {s}$$

Answer

$$0.7 {~m} / {s}$$

Answer

$$0.9 {~m} / {s}$$

Answer

$$0.2 {~m} / {s}$$

Question 2

Case-Study 2: Read the following passage and answer the questions given below.

![](http://admin.getprephub.com/media/editor/mh37_20221009215707956362.png)

In an elliptical sport field the authority wants to design a rectangular soccer field with the maximum possible area. The sport field is given by the graph of $$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$$

If the length and the breadth of the rectangular field be $$2 x$$ and $$2 y$$ respectively, then find the area function in terms of $$x$$.

Accepted Answer

Covalent bond

Answer

$$\frac{4 b x \sqrt{a^{2}-x^{2}}}{a}$$

Answer

$$\frac{3 b x \sqrt{a^{3}-x^{4}}}{a}$$

Answer

$$\frac{2 b x \sqrt{a^{4}-x^{3}}}{a}$$

Answer

None of the above

Question 3

Case-Study 2: Read the following passage and answer the questions given below.

![](http://admin.getprephub.com/media/editor/mh37_20221009215707956362.png)

In an elliptical sport field the authority wants to design a rectangular soccer field with the maximum possible area. The sport field is given by the graph of $$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$$

Find the critical point of the function.

Accepted Answer

Covalent bond

Answer

$$\frac{a}{\sqrt{2}}$$

Answer

$$\frac{b}{\sqrt{2}}$$

Answer

$$\frac{ab}{\sqrt{2}}$$

Answer

None of the above

Question 4

Case-Study 1: Read the following passage and answer the questions given below.
![](http://admin.getprephub.com/media/editor/mh36_20221009215356894142.png)

The temperature of a person during an intestinal illness is given by $$f(x)=-0.1 x^{2}+m x+98.6,0 \leq x \leq 12$$, m being a constant, where $$f(x)$$ is the temperature in $${ }^{\circ} {F}$$ at $${x}$$ days.

Is the function differentiable in the interval $$(0,12)$$ ? Justify your answer.

Accepted Answer

Covalent bond

Answer

$$(0,12)$$

Answer

$$(1,2)$$

Answer

$$(4,18)$$

Answer

$$(3,15)$$

Question 5

Case-Study 1: Read the following passage and answer the questions given below.

![](http://admin.getprephub.com/media/editor/mh36_20221009215356894142.png)

The temperature of a person during an intestinal illness is given by $$f(x)=-0.1 x^{2}+m x+98.6,0 \leq x \leq 12$$, m being a constant, where $$f(x)$$ is the temperature in $${ }^{\circ} {F}$$ at $${x}$$ days.

If 6 is the critical point of the function, then find the value of the constant $$m$$.

Accepted Answer

Covalent bond

Answer

$$1.2$$

Answer

$$6.8$$

Answer

$$3.9$$

Answer

$$4.9$$

Application Of Derivatives Cbse Class 12 Maths Problems and Solutions

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