Find the intervals in which the following functions are strictly

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 Multiple Choice QuestionsShort Answer Type

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171.

Find the intervals in which the following functions are strictly increasing or decreasing:
6 – 9x – x 2


Let f(x) = 6 – 9x – x 2                               therefore space space space space straight f apostrophe left parenthesis straight x right parenthesis space equals space minus 9 minus 2 straight x
Now,     straight f apostrophe left parenthesis straight x right parenthesis greater than 0 space space space when space minus 2 straight x minus 9 greater than 0 space space straight i. straight e. space space space when space straight x space less than negative 9 over 2
therefore space space space straight f left parenthesis straight x right parenthesis space is space increasing space for space straight x less than negative 9 over 2
therefore space space space space straight f left parenthesis straight x right parenthesis space is space increasing space in space open parentheses negative infinity comma space space fraction numerator negative 9 over denominator 2 end fraction close parentheses.
Also comma space straight f apostrophe left parenthesis straight x right parenthesis space less than space 0 space space when space minus 2 straight x minus 9 less than 0 space space space straight i. straight e. space when space straight x greater than negative 9 over 2
therefore space space space space straight f left parenthesis straight x right parenthesis space is space increasing space for space straight x space greater than negative 9 over 2
therefore space space space space space space straight f left parenthesis straight x right parenthesis space is space decreasing space in space open parentheses negative 9 over 2 comma space space infinity close parentheses.

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172.

Find the intervals in which the following function is increasing or decreasing:
x3 – 6x2 + 9x + 15. 

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173.

Find the intervals in which the following function f(x) is
(a) increasing      (b) decreasing:
f (x) = 2x3 – 9x2 + 12x + 15

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174.

Determine the values of x for which the function f(x)  =  2x3 – 24x + 5 is increasing or decreasing.

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175.

Find the intervals in which the functions f (x) = 2x3 – 15x2 + 36x + 1 is strictly increasing or decreasing. Also find the points on which the tangents are parallel to the x-axis.

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176.

Find the intervals in which the function
f(x) = x3 – 12x2 + 36x + 17 is
(a) strictly increasing    (b) strictly decreasing 

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177.

Find the intervals in which the function f (x) = 2x– 15x2 + 36x + 1 is
(a) strictly increasing     (b) strictly decreasing 

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178.

Find the intervals in which the following functions are strictly increasing or strictly decreasing:
x3 – 6x2 – 36x +4

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179.

Find the intervals in which the following functions are strictly increasing or strictly decreasing:
2x3 – 15x2 + 36x + 6

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180.

Find the intervals in which the following functions are strictly increasing or strictly decreasing:
6 + 12x + 3x– 2x3 

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