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Geometric Interpretation of Def.Int as Limit of Sum

Find the inte...

Question

Find the intervals of monotonicity of the following functions.
$f (x) = - x^{3} + 6 x^{2} - 9 x - 2$

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Solution

$f' (x) = - 3 x^{2} + 12 x - 9 f' (x) \geq 0 - 3 x^{2} + 12 x - 9 \geq 0 x^{2} - 4 x + 3 \leq 0 x^{2} - 3 x - x + 3 \leq 0 (x - 3) (x - 1) \leq 0 x \in [- 3, 1] (x - 3) (x - 1) \geq 0 x \in (- \infty, 1) U (3, \infty)$

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