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The interval in which $f(x)=x^3-2x^2-9x+20$ is strictly increasing , strictly decreasing. |
$(–∞, –1) ∪ (–3 , ∞), (1, 3)$ $(–∞, –1) ∪ (3 , ∞), (–1, 3)$ $(–∞, 1) ∪ (3 , ), (1, 3)$ $(–∞, 2) ∪ (3 , ∞), (–1, 3)$ |
$(–∞, –1) ∪ (3 , ∞), (–1, 3)$ |
Given $f(x)=x^3-2x^2-9x+20$ $f'(x)=3x^2-6x-9$ $⇒f'(x)=3(x^2-2x-3)$ $⇒f'(x) = 3(x −3)(x +1)$ Using number line method, as shown in figure
$⇒f'(x) > 0$ for $x∈(−∞,−1)∪(3,∞)$ $⇒f'(x) < 0$ for $x∈(−1,3)$ |
