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Maths-

General

Easy

Question

The number of values of $x$ where $f open parentheses x close parentheses equals cos invisible function application x plus cos invisible function application square root of 2 x$ attains its maximum is

1
0
2
Infinite

The correct answer is: 1

Given, $f open parentheses x close parentheses equals cos invisible function application x plus cos invisible function application square root of 2 x$
$rightwards double arrow blank f to the power of ´ end exponent open parentheses x close parentheses equals negative sin invisible function application x minus square root of 2 sin invisible function application square root of 2 x$

$rightwards double arrow blank f to the power of ´ ´ end exponent open parentheses x close parentheses equals negative cos invisible function application x minus 2 cos invisible function application square root of 2 x$

For extremum value, put $f to the power of ´ end exponent open parentheses x close parentheses equals 0$

$rightwards double arrow blank minus sin invisible function application x minus square root of 2 sin invisible function application square root of 2 x equals 0 blank rightwards double arrow blank x equals 0$

$therefore$ At $x equals 0 comma blank f to the power of ´ ´ end exponent open parentheses x close parentheses less than 0$ , maxima

$therefore blank f left parenthesis x right parenthesis$ Is maximum only once.

Related Questions to study

A function $f$ is defined by $f open parentheses x close parentheses equals 2 plus open parentheses x minus 1 close parentheses to the power of 2 divided by 3 end exponent$ in [0, 2]. Which of the following is not correct?

A function $f$ is defined by $f open parentheses x close parentheses equals 2 plus open parentheses x minus 1 close parentheses to the power of 2 divided by 3 end exponent$ in [0, 2]. Which of the following is not correct?

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Let $f open parentheses x close parentheses equals square root of x minus 1 end root plus square root of x plus 24 minus 10 square root of x minus 1 end root end root comma blank 1 less or equal than x less or equal than 26$ be real valued function, then $f to the power of ´ end exponent left parenthesis x right parenthesis$ for $1 less than x less than 26$ is

parallel

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parallel

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The equation of tangent to the curve $y equals b e to the power of negative x divided by a end exponent$ at the point where it crosses $blank y minus$ axis, is

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parallel

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If $theta$ is the angle between the curves $x y equals 2$ and $x to the power of 2 end exponent plus 4 y equals 0$ , then $tan invisible function application theta$ is equal to

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parallel

Vector sum of two forces of 10 N and 6 N cannot be

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The vector sum of the forces of 10 N and 6 N can be

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parallel

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