Find the maximum and minimum values, if any, of the following fu

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 Multiple Choice QuestionsShort Answer Type

211.

Find the maximum and minimum values, if any, of the following functions without using the derivatives:
– (x – 1)+ 10

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212.

Find the maximum and minimum values, if any, of the following functions without using the derivatives:
(2 x – 1)+ 3

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213.

Find the maximum and minimum values, if any, of the following functions without using the derivatives:
4x2 – 4x + 11


 Let space space space straight f left parenthesis straight x right parenthesis space equals space 4 straight x squared minus 4 straight x plus 11 space space equals space 4 left parenthesis straight x squared minus straight x right parenthesis space plus 11 space equals space 4 space open parentheses straight x squared minus straight x plus 1 fourth close parentheses plus left parenthesis 11 minus 1 right parenthesis
space space space space space space space space space equals 4 space open parentheses straight x minus 1 half close parentheses squared plus 10
Now,   open parentheses straight x minus 1 half close parentheses squared space greater or equal than space space space 0 space space space space space for all space space straight x space space space element of space space space straight R


therefore space space space 4 open parentheses straight x minus 1 half close parentheses squared space greater or equal than space space 0 space space space space space for all space straight x space space space element of space space straight R space space space space space space space space space space space space space space space rightwards double arrow space space space space space space 4 space open parentheses straight x minus 1 half close parentheses squared plus 10 space greater or equal than space 10 space space space space for all space space straight x space element of space space straight R
rightwards double arrow space space space space straight f left parenthesis straight x right parenthesis space greater or equal than space 10 space space space space space for all space space straight x space space space element of space space space straight R
therefore space space space minimum space value space of space straight f left parenthesis straight x right parenthesis space is space 10. space It space has space no space maximum space value.
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214.

Find the maximum or minimum values, if any, of the following functions without using the derivatives:
x3 + 1

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215.

Find the maximum or minimum values, if any, of the following functions without using the derivatives:
| x + 2 |

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216.

Find the maximum or minimum values, if any, of the following functions without using the derivatives:
– | x + 1 | + 3

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217.

Find the maximum or minimum values, if any, of the following functions without using the derivatives:
sin (2x + 3)

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218.

Find the maximum or minimum values, if any, of the following functions without using the derivatives:
sin 2x + 5

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219.

Find the maximum or minimum values, if any, of the following functions without using the derivatives:
|sin 4x + 3|

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220.

Find the maximum or minimum values, if any, of the following functions without using the derivatives:
sin (sin x)

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