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The interval on which the function $f(x) = x^3 + 2x^2-1$ is decreasing, is |
$(-∞,-4/3)$ $[0,∞)$ $[-4/3,0)$ $[-4/3,∞)$ |
$[-4/3,0)$ |
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: $x \in [-\frac{4}{3}, 0)$ |
