Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 10

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Which of the following statement(s) is/are correct?

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Important Questions on Application of Derivatives

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 11

Which of the following option(s) is/are correct with respect to the function

f (x) = x^{4} - \frac{4}{3} x^{3} + 2 x^{2} + a x + b

?

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 12

Consider the functions

f (x) = \{\begin{cases} |x|, x \leq - 1 \\ x^{\frac{1}{5}} - 1 < x \leq 1 \\ {(2 - x)}^{3}, x > 1 \end{cases}

and

g (x) = \frac{1}{{(x + 2)}^{3}} - 2 x - \cos x

. Let

p

be the number of critical points on the graph of

f (x)

and

q

be the number of solutions of

g (x) = 0

, then which of the following option(s) is/are correct?

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 13

Let

A

be the maximum area of the incircle of the right-angled triangle with hypotenuse of length

(\sqrt{2} + 1)

units and

B

be the minimum area of the circumcircle of the right-angled triangle with area

4

square units. Then, which of the following option(s) is/are correct?

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 14

The length of the portion of a tangent line to the curve

x^{2 / 3} + y^{2 / 3} = 4

at the point

P

, cut off by the coordinate axes, is

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 15

Which of the following statement(s) is/are correct?

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 16

Which of the following statement(s) is/are correct for the function

f (x) = \frac{x^{2} - 2}{3 x^{2} - 9}

?

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 4

The least natural number

a

for which

x + a x^{- 2} > 2 \forall x \in (0, \infty)

is:

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 5

Any tangent at a point

P (x, y)

to the ellipse

\frac{x^{2}}{8} + \frac{y^{2}}{18} = 1

meets the positive co-ordinate axes in the points

A

and

B

such that the area of the

∆ O A B

is least, then the point

P

is of the form

(m, n)

where

m + n + 10

is