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Maths-

General

Easy

Question

The greatest, the least values of the function, $f left parenthesis x right parenthesis equals 2 minus square root of 1 plus 2 x plus x to the power of 2 end exponent end root comma$ $x element of left square bracket 21 right square bracket$ are respectively

2, 1
$2,$ -1
2, 0
none

The correct answer is: 2, 0

In the question minimum and maximum values are asked
$G i v e n space e q u a t i o n space f left parenthesis x right parenthesis equals 2 minus square root of 1 plus 2 x plus x squared end root R a n g e space o f space x squared plus 2 x plus 1 D equals 4 minus 4 equals 0 M i n i m u m space v a l u e space equals space fraction numerator negative D over denominator 4 a end fraction equals 0 space x squared plus 2 x plus 1 greater or equal than 0 f apostrophe left parenthesis x right parenthesis equals 2 x plus 2 f left parenthesis x right parenthesis space i s space i n c r e a sin g space f u n c t i o n space i n space left square bracket negative 2 comma 1 right square bracket x squared plus 2 x plus 1 equals 1 plus 2 plus 1 equals 4 0 less or equal than square root of space x squared plus 2 x plus 1 end root less or equal than square root of 4 0 less or equal than square root of space x squared plus 2 x plus 1 end root less or equal than 2 0 greater or equal than negative square root of space x squared plus 2 x plus 1 end root greater or equal than negative 2 B y space a d d i n g space 2 space o n space b o t h space s i d e s 2 greater or equal than 2 minus square root of space x squared plus 2 x plus 1 end root greater or equal than 0 m a x i m u m space v a l u e space equals 2 comma space L e a s t space v a l u e equals 0 A n s equals left parenthesis 2 comma 0 right parenthesis$

Hence the final answer is (2,0)

Related Questions to study

Suppose that $f$ is differentiable for allx and that $f to the power of ’ end exponent left parenthesis x right parenthesis less or equal than 2$ for all x If $f left parenthesis 1 right parenthesis equals 2$ and f(4)=8 then f(2) has the value equal to

Hence f(2)=4 is the suitable option

Suppose that $f$ is differentiable for allx and that $f to the power of ’ end exponent left parenthesis x right parenthesis less or equal than 2$ for all x If $f left parenthesis 1 right parenthesis equals 2$ and f(4)=8 then f(2) has the value equal to

Hence f(2)=4 is the suitable option

$f left parenthesis x right parenthesis equals not stretchy integral subscript blank superscript left parenthesis end superscript left parenthesis 2 minus fraction numerator 1 over denominator 1 plus x to the power of 2 end exponent end fraction minus fraction numerator 1 over denominator square root of 1 plus x to the power of 2 end exponent end root end fraction right parenthesis right parenthesis$ dxthenfis‐

$f left parenthesis x right parenthesis equals not stretchy integral subscript blank superscript left parenthesis end superscript left parenthesis 2 minus fraction numerator 1 over denominator 1 plus x to the power of 2 end exponent end fraction minus fraction numerator 1 over denominator square root of 1 plus x to the power of 2 end exponent end root end fraction right parenthesis right parenthesis$ dxthenfis‐

The tangent to the curve $3 x y to the power of 2 end exponent minus 2 x to the power of 2 end exponent y equals 1$ at (1,1) meets the curve again at the point‐

The final answer is option B

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The final answer is option B

parallel

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