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Question
Find the intervals in which the following functions are strictly increasing or decreasing:
6 − 9x − x2
Solution
f(x) = 6 - 9x - x2
f'(x) = - 9x - 2x = -(2x + 9)
f'(x) = 0 ⇒ (2x + 9) = 0 ⇒ x = - `9/2`
The point x = `- 9/2` divides the number line into two parts, intervals `(- oo, - 9/2)` and `(- 9/2, oo)`.
In the interval `(- oo, - 9/2)`, f'(x) = (-)(-) = + Positive
Hence, the function f is continuously increasing.
In the interval `(- 9/2, oo)`, f'(x) = (-)(+) = - Negative
Hence, the function f is continuously decreasing.
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