Short Quiz

Question 1 of 5

NCERT Exemplar

$y=x(x-3)^2$ decreases for the values of $x$ given by :

A $1<x<3$ B $x<0$ C $x>0$ D $0<x<\frac{3}{2}$

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Question 2 of 5

NCERT Exemplar

A company's marginal cost is the derivative of its cost function, $C^{\prime}(x)$. If $C^{\prime}(100)=$ 15, what does this signify?

A The total cost of producing 100 items is $\$ 15$. B The average cost per item is $\$ 15$. C The cost to produce the 101st item is approximately $\$ 15$. D The company makes a profit of $\$ 15$ on the 100th item.

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Question 3 of 5

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To find the dimensions of a rectangle with a fixed perimeter that has the maximum possible area, one should look for a point where:

A The second derivative of the area function is positive. B The first derivative of the area function is zero and the second derivative is negative. C The first derivative of the area function is positive. D The area function itself is equal to zero.

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Question 4 of 5

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$\mathrm{f}(\mathrm{x})=\mathrm{x}^{\mathrm{x}}$ has a stationary point at

A $\mathrm{x}=\mathrm{e}$ B $x=\frac{1}{e}$ C $x=1$ D $x=\sqrt{e}$

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Question 5 of 5

NCERT Exemplar

The sides of an equilateral triangle are increasing at the rate of 2 $\mathrm{cm} / \mathrm{sec}$. The rate at which the area increases, when side is 10 cm is:

A $10 \mathrm{~cm}^2 / \mathrm{s}$ B $3 \mathrm{~cm}^2 / \mathrm{s}$ C $10 \sqrt{\mathbf{3}} \mathrm{~cm}^2 / \mathrm{s}$ D $\frac{10}{3} \mathrm{~cm}^2 / \mathrm{s}$

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