GATE DA topic:calculus-optimization PYQs & Answers

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topic:calculus-optimization

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Questions 1–10 of 14. Imported answers require independent review unless marked reviewed.

Topic practice 14 questionsPage 1 of 2

Let

be a function defined on

Which of the following statements is/are correct?

Your answerSelect all correct options. You can choose more than one.

has exactly two roots in

has a minimum at 2 only.

has maximum at 0 only.

has a root at 1.

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The value of

is ____________ . (Answer in integer)

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If a real variable

satisfies

, then the value of

is:

Your answerChoose one option.

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Let

. Let

denote the

th derivative of

evaluated at

. What is the value of

? (Note:

denotes factorial)

Your answerChoose one option.

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Consider two functions

and

. Both functions are differentiable at a point

. Which of the following functions is/are ALWAYS differentiable at

? The symbol

denotes product and the symbol

denotes composition of functions.

Your answerSelect all correct options. You can choose more than one.

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____________ (Round off to one decimal place)

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Consider the function

. Which of the following statements is/are correct?

Your answerSelect all correct options. You can choose more than one.

The maximum value of

is attained at

The minimum value of

is attained at

The maximum value of

The minimum value of the derivative of

is attained at

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Let

be a twice-differentiable function and suppose its second derivative satisfies

for all

. Which of the following statements is/are ALWAYS correct?

Your answerSelect all correct options. You can choose more than one.

has a local minima

There does not exist

and

, such that

has at most one global minimum

has at most one local minimum

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Let

be such that

for all

. Then

______ (Answer in integer)

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For any twice differentiable function

, if at some

and

, then the function

necessarily has a _____ at

. Note:

denotes the set of real numbers.

Your answerChoose one option.

local minimum

global minimum

local maximum

global maximum

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GATE DA topic:calculus-optimization PYQs

How to practice topic:calculus-optimization

Question 27

Question 35

Question 9

Question 14

Question 24

Question 32

Question 49

Question 51

Question 59

Question 15