Find the local maxima or local minima, if any, of the following

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 Multiple Choice QuestionsShort Answer Type

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241.

Find the local maxima or local minima, if any, of the following functions using the first derivative test only. Find also the local maximum and the local minimum values, as the case may be:
straight h left parenthesis straight x right parenthesis space equals space sinx plus cosx comma space 0 space less than space straight x space less than space straight pi over 2






Let straight f left parenthesis straight x right parenthesis space equals space sinx plus cosx space comma space 0 space space less than space straight x less than straight pi over 2
therefore space space space straight f apostrophe left parenthesis straight x right parenthesis space equals space cosx minus space sinx
Now,  straight f apostrophe left parenthesis straight x right parenthesis space equals space 0 space space space space rightwards double arrow space space space space cos space straight x minus sin space straight x space equals space 0 space space space space rightwards double arrow space space space sinx space equals space cosx space space rightwards double arrow space space space tanx space equals space 1 space space space rightwards double arrow space space straight x space equals space straight pi over 4
Now,
   straight f apostrophe left parenthesis straight x right parenthesis space equals space square root of 2 space open parentheses fraction numerator 1 over denominator square root of 2 end fraction cosx space minus fraction numerator 1 over denominator square root of 2 end fraction sinx close parentheses space equals space square root of 2 space open parentheses cosx space cos straight pi over 4 minus sinx space sin straight pi over 4 close parentheses
space space space space space space space space space space equals square root of 2 space cos space open parentheses straight x plus straight pi over 4 close parentheses
When space straight x less than straight pi over 4 space slightly comma space space straight f apostrophe left parenthesis straight x right parenthesis space equals space plus ve
When space straight x greater than space straight pi over 4 space slightly comma space straight f apostrophe left parenthesis straight x right parenthesis space equals space minus ve
therefore space space space space at space straight x space equals space straight pi over 4 comma space space straight f apostrophe left parenthesis straight x right parenthesis space changes space from space plus ve space to space minus ve
therefore space space space straight f left parenthesis straight x right parenthesis space has space local space maxima space at space straight x space equals space straight pi over 4
and space local space maximum space value space space equals space sin space space straight pi over 4 plus space cos space straight pi over 4
space space space space space space space space space space space space space space space space space equals fraction numerator 1 over denominator square root of 2 end fraction plus fraction numerator 1 over denominator square root of 2 end fraction space equals space fraction numerator 2 over denominator square root of 2 end fraction space equals space square root of 2

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 Multiple Choice QuestionsLong Answer Type

242.

Find the local maxima or local minima, if any, of following functions using the first derivative test only. Find also the local maximum and the local minimum values, as the case may be:
sinx minus cosx comma space space 0 less than straight x less than 2 straight pi






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 Multiple Choice QuestionsShort Answer Type

243.

Find the local maxima or local minima, if any, of following functions using the first derivative test only. Find also the local maximum and the local minimum values, as the case may be:
f(x) = x3 – 6x2 + 9x + 15



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 Multiple Choice QuestionsLong Answer Type

244.

Find the local maxima or local minima, if any, of following functions using the first derivative test only. Find also the local maximum and the local minimum values, as the case may be:
f(x) = (x – 1)(x + 2)2

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 Multiple Choice QuestionsShort Answer Type

245.

Find the local maxima or local minima, if any, of following functions using the first derivative test only. Find also the local maximum and the local minimum values, as the case may be:
straight g left parenthesis straight x right parenthesis space equals straight x over 2 plus 2 over straight x comma space space space straight x greater than 0

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246.

Find the local maxima or local minima, if any, of following functions using the first derivative test only. Find also the local maximum and the local minimum values, as the case may be:
straight g left parenthesis straight x right parenthesis space equals space fraction numerator 1 over denominator straight x squared plus 2 end fraction space equals space left parenthesis straight x squared plus 2 right parenthesis to the power of negative 1 end exponent


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247.

Find the local maxima or local minima, if any, of following functions using the first derivative test only. Find also the local maximum and the local minimum values, as the case may be:
straight f left parenthesis straight x right parenthesis space equals space straight x square root of 1 minus straight x end root comma space 0 less than straight x less than 1



74 Views

 Multiple Choice QuestionsLong Answer Type

248.

Find the local maxima or local minima, if any, of following functions using the first derivative test only. Find also the local maximum and the local minimum values, as the case may be:
sin to the power of 4 straight x plus cos to the power of 4 straight x comma space space space 0 less than straight x less than straight pi over 2




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249.

Find the local maxima or local minima, if any, of following functions using the first derivative test only. Find also the local maximum and the local minimum values, as the case may be:
sin 2 straight x minus straight x comma space space minus straight pi over 2 less or equal than straight x less or equal than straight pi over 2





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 Multiple Choice QuestionsShort Answer Type

250.

Find the local maxima or local minima, if any, of following functions using the first derivative test only. Find also the local maximum and the local minimum values, as the case may be:
left parenthesis straight x minus 3 right parenthesis to the power of 4






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