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

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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



Let 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 left parenthesis straight x squared plus 2 right parenthesis to the power of negative 1 end exponent
therefore space space straight g apostrophe left parenthesis straight x right parenthesis space equals space minus left parenthesis straight x squared plus 2 right parenthesis space squared space space left parenthesis 2 straight x right parenthesis space equals space minus fraction numerator 2 straight x over denominator left parenthesis straight x plus 2 right parenthesis squared end fraction
    straight g apostrophe left parenthesis straight x right parenthesis space equals space 0 space space space space space rightwards double arrow space space space space space minus fraction numerator 2 straight x over denominator left parenthesis straight x squared plus 2 right parenthesis squared end fraction space equals space 0 space space space space rightwards double arrow space space space space straight x space equals space 0
When space straight x space less than 0 space space space slightly comma space space then space space straight g apostrophe left parenthesis straight x right parenthesis space equals space minus 2 fraction numerator left parenthesis negative ve right parenthesis over denominator plus ve end fraction space equals space plus ve

When straight x greater than 0 space slightly comma space space space then space straight f apostrophe left parenthesis straight x right parenthesis space equals space minus 2 fraction numerator left parenthesis plus ve right parenthesis over denominator plus ve end fraction space equals space minus ve

therefore space space space straight f apostrophe left parenthesis straight x right parenthesis space changes space from space plus ve space to space minus ve space as space straight x space passes space through space 0.
therefore space space space straight x space equals space 0 space is space straight a space point space of space local space maxima space and space this space local space max space value space space equals space fraction numerator 1 over denominator 0 plus 2 end fraction equals 1 half.

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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





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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