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



101 Views

 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

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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


Let straight g left parenthesis straight x right parenthesis space equals space straight x over 2 plus 2 over straight x comma space space space straight x greater than 0
          straight g apostrophe left parenthesis straight x right parenthesis space equals space 1 half minus 2 over straight x squared
straight g apostrophe left parenthesis straight x right parenthesis space equals space 0 space space space space rightwards double arrow space space space space 1 half minus 2 over straight x squared space equals space 0 space space space space space rightwards double arrow space space space space straight x squared minus 4 space equals space 0 space space space space rightwards double arrow space space space space straight x space equals space 2 comma space minus 2
              But space straight x space greater than 0 space space space left parenthesis given right parenthesis

therefore space space space straight x space equals space 2 space is space the space only space critical space point. space
space space space space Now space space straight g apostrophe left parenthesis straight x right parenthesis space equals space fraction numerator straight x squared minus 4 over denominator 2 straight x squared end fraction space equals fraction numerator left parenthesis straight x minus 2 right parenthesis thin space left parenthesis straight x plus 2 right parenthesis over denominator 2 straight x squared end fraction
space space space When space straight x less than 2 space space slightly comma space space straight g apostrophe left parenthesis straight x right parenthesis space equals space fraction numerator left parenthesis negative right parenthesis thin space left parenthesis plus right parenthesis over denominator plus end fraction space equals space minus ve
space space space space When space straight x greater than 2 space slightly space straight g apostrophe left parenthesis straight x right parenthesis space equals space fraction numerator left parenthesis plus right parenthesis thin space left parenthesis plus right parenthesis over denominator plus end fraction space equals space plus ve
space space space space space therefore space space space space at space straight x space equals space 2 comma space space straight g apostrophe left parenthesis straight x right parenthesis space changes space from space minus ve space to space space plus ve
space space space space space therefore space straight g left parenthesis straight x right parenthesis space has space local space minimum space value space at space straight x space equals space 2 space and space
space space space space local space minimum space value space at space straight x space equals 2 space and space
space space space local space minimum space value space space equals space 2 over 2 plus 2 over 2 space equals space 1 plus 1 space equals space 2

76 Views

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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


71 Views

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





78 Views

 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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