The interval in which $f(x)=x^3-2x^2-9x+20$ is strictly increasing , strictly decreasing.
Answer & explanation
Correct answer: option 2
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 $x∈(−1,3)$