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CBSE Class 12-science Answered

Please answer this question. 
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Asked by dineshchem108 | 09 Oct, 2019, 07:55: PM
answered-by-expert Expert Answer
Let f(x)=e to the power of left parenthesis 2 plus square root of 3 cos x plus sin x right parenthesis end exponent
f apostrophe left parenthesis x right parenthesis equals e to the power of open parentheses 2 plus square root of 3 cos x plus sin x close parentheses end exponent open parentheses negative square root of 3 sin x plus cos x close parentheses T a k e space f apostrophe left parenthesis x right parenthesis equals 0 rightwards double arrow e to the power of open parentheses 2 plus square root of 3 cos x plus sin x close parentheses end exponent open parentheses negative square root of 3 sin x plus cos x close parentheses A s space e to the power of x not equal to 0 rightwards double arrow negative square root of 3 sin x plus cos x equals 0 rightwards double arrow tan x equals fraction numerator 1 over denominator square root of 3 end fraction rightwards double arrow x equals n straight pi plus straight pi over 6 equals straight pi over 6 comma space fraction numerator 7 straight pi over denominator 6 end fraction comma... straight f " left parenthesis straight x right parenthesis equals straight e to the power of open parentheses 2 plus square root of 3 cosx plus sinx close parentheses end exponent open parentheses negative square root of 3 cosx minus sinx close parentheses plus open parentheses negative square root of 3 sinx plus cosx close parentheses straight e to the power of open parentheses 2 plus square root of 3 cosx plus sinx close parentheses end exponent open parentheses negative square root of 3 sinx plus cosx close parentheses straight f " open parentheses straight pi over 6 close parentheses equals straight e to the power of open parentheses 2 plus 3 over 2 plus 1 half close parentheses end exponent open parentheses negative 3 over 2 minus 1 half close parentheses plus open parentheses negative fraction numerator square root of 3 over denominator 2 end fraction plus fraction numerator square root of 3 over denominator 2 end fraction close parentheses straight e to the power of open parentheses 2 plus 3 over 2 plus 1 half close parentheses end exponent open parentheses negative fraction numerator square root of 3 over denominator 2 end fraction plus fraction numerator square root of 3 over denominator 2 end fraction close parentheses space space space space space space space space space space space equals negative 2 straight e to the power of 4 less than 0 So comma space straight pi over 6 space gives space the space maximum space value Now comma space straight f " open parentheses fraction numerator 7 straight pi over denominator 6 end fraction close parentheses equals straight e to the power of open parentheses 2 minus 3 over 2 minus 1 half close parentheses end exponent open parentheses 3 over 2 plus 1 half close parentheses plus open parentheses fraction numerator square root of 3 over denominator 2 end fraction minus fraction numerator square root of 3 over denominator 2 end fraction close parentheses straight e to the power of open parentheses 2 minus 3 over 2 minus 1 half close parentheses end exponent open parentheses fraction numerator square root of 3 over denominator 2 end fraction minus fraction numerator square root of 3 over denominator 2 end fraction close parentheses equals 2 straight e to the power of 0 equals 2 greater than 0 So comma space fraction numerator 7 straight pi over denominator 6 end fraction space is space the space minima Thus comma space the space minumum space value space is space straight f open parentheses fraction numerator 7 straight pi over denominator 6 end fraction close parentheses equals straight e to the power of open parentheses 2 plus square root of 3 cos fraction numerator 7 straight pi over denominator 6 end fraction plus sin fraction numerator 7 straight pi over denominator 6 end fraction close parentheses end exponent equals straight e to the power of 0 equals 1
Answered by Renu Varma | 10 Oct, 2019, 10:45: AM

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