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

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 Multiple Choice QuestionsShort Answer Type

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





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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






72 Views

 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

76 Views

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




73 Views

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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






Let space straight f left parenthesis straight x right parenthesis space equals space sin space 2 straight x space minus straight x comma space space space minus straight pi over 2 less or equal than straight x less or equal than straight pi over 2
therefore space space space straight f apostrophe left parenthesis straight x right parenthesis space equals space 2 space cos space 2 straight x minus 1
space space space space straight f apostrophe left parenthesis straight x right parenthesis space equals space 0 space space space space space rightwards double arrow space space space space 2 space cos space 2 straight x space minus 1 space space equals space 0 space space space space space rightwards double arrow space space space cos space 2 straight x space equals space 1 half
rightwards double arrow space space space space cos space 2 straight x space equals space cos space straight pi over 3 comma space space cos space open parentheses negative straight pi over 3 close parentheses
therefore space space space space 2 straight x space equals space straight pi over 3 comma space space space space fraction numerator negative straight pi over denominator 3 end fraction space space space space space space space space rightwards double arrow space space space space straight x space equals space straight pi over 6 comma space space space minus straight pi over 6
When space straight x less than negative straight pi over 6 space slightly comma space space straight f apostrophe left parenthesis straight x right parenthesis space equals space minus ve
When space straight x space greater than negative straight pi over 6 space slightly comma space straight f apostrophe left parenthesis straight x right parenthesis space equals space plus ve
therefore space space space at space straight x space equals space minus straight pi over 6 comma space space space straight f apostrophe left parenthesis straight x right parenthesis space changes space from space minus ve space to space ve
therefore space space space straight f left parenthesis straight x right parenthesis space has space straight a space local space minima space at space straight x space equals space minus straight pi over 6
and space this space local space minimum space value space space equals space sin space open parentheses negative straight pi over 3 close parentheses minus open parentheses negative straight pi over 6 close parentheses space equals space minus sin space straight pi over 3 space plus space straight pi over 6 space equals negative fraction numerator square root of 3 over denominator 2 end fraction plus straight pi over 6
When space straight x less than straight pi over 6 space slightly comma space straight f apostrophe left parenthesis straight x right parenthesis space equals space plus ve
When space straight x greater than straight pi over 6 space slightly comma space space straight f apostrophe left parenthesis straight x right parenthesis space equals space minus ve
therefore space space space at space straight x space equals space straight pi over 6 comma space space space straight f 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 6
and space this space local space maximum space value space space equals space sin space straight pi over 3 minus straight pi over 6 space equals space fraction numerator square root of 3 over denominator 2 end fraction minus straight pi over 6
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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






87 Views

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