Find the absolute maximum value and the absolute minimum value o

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 Multiple Choice QuestionsShort Answer Type

221.

Find the maximum or minimum values, if any, of the following functions without using the derivatives:
16x– 16x + 28

 
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222.

Prove that the following functions do not have maxima or minima:
f(x) = ex

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223.

Prove that the following functions do not have maxima or minima:
g(x) = log x

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224.

Prove that the following functions do not have maxima or minima:
h(x) = x3 + x2 + x + 1

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225.

Find the absolute maximum value and the absolute minimum value of 
straight f left parenthesis straight x right parenthesis space equals space 1 third straight x cubed minus 3 straight x squared plus 5 straight x plus 8 space in space left square bracket 0 comma space 4 right square bracket.

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226.

Find the absolute maximum and minimum values of a function f is given by
f (x) = 2x3 – 15x2 + 36x + 1 on the interval of [1, 5].

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 Multiple Choice QuestionsLong Answer Type

227. Find absolute maximum and minimum values of a function f given by
straight f left parenthesis straight x right parenthesis space equals space 12 straight x to the power of 4 over 3 end exponent space minus space 6 straight x to the power of 1 third end exponent comma space space space straight x space element of space space space open square brackets negative 1 comma space 1 close square brackets
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 Multiple Choice QuestionsShort Answer Type

228.

Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals:
straight f left parenthesis straight x right parenthesis space equals space straight x cubed comma space space space straight x space element of space left square bracket negative 2 comma space space 2 right square bracket

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229.

Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals:
straight f left parenthesis straight x right parenthesis space equals space sin space straight x plus space cosx comma space space straight x space space element of space space left square bracket 0 comma space straight pi right square bracket

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230.

Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals:
straight f left parenthesis straight x right parenthesis space equals space 4 straight x minus 1 half straight x squared comma space space space straight x space element of space open square brackets negative 2 comma space space 9 over 2 close square brackets



Let straight f left parenthesis straight x right parenthesis space equals space 4 straight x minus 1 half straight x squared
It is differentiable for all x in open square brackets negative 2 comma space space space 9 over 2 close square brackets
   straight f apostrophe left parenthesis straight x right parenthesis space equals space 4 minus straight x
straight f apostrophe left parenthesis straight x right parenthesis space equals space 0 space space space rightwards double arrow space space space 4 minus straight x space equals space 0 space space space space space rightwards double arrow space space space straight x space equals space 4 space element of space space open square brackets negative 2 comma space space space 9 over 2 close square brackets
space space space straight f left parenthesis 4 right parenthesis space equals space 16 minus 1 half cross times 16 space equals space 16 minus 8 space equals space 8
space straight f left parenthesis negative 2 right parenthesis space equals space minus 8 minus 1 half left parenthesis negative 2 right parenthesis squared space equals space minus 8 minus 2 space equals space minus 10
straight f open parentheses 9 over 2 close parentheses space equals space 4 space open parentheses 9 over 2 close parentheses space minus space 1 half open parentheses 9 over 2 close parentheses squared space equals space 18 minus 81 over 8 space equals space 63 over 8 space equals space 7 7 over 8
therefore space space space absolute space max. space value space space equals space 8 space space and space aboslute space min. space value space space equals space minus 10

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