The interval on which the function $f(x) = x^3 + 2x^2-1$ is decreasing, is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $[-4/3,0)$
Given: $f(x) = x^3 + 2x^2 - 1$
Find $f'(x)$:
$f'(x) = 3x^2 + 4x$
Set $f'(x) < 0$ for decreasing interval:
$3x^2 + 4x < 0$
$x(3x + 4) < 0$
Solution: $x \in [-\frac{4}{3}, 0)$