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

Solution

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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Application Of Derivatives

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

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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For Daily Free Study Material Join wiredfaculty

Application Of Derivatives

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

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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