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Choose the correct option.
The function f(x) = x³ - 3x is strictly decreasing on:
The function $f(x) = x^3 - 3x$ is strictly decreasing on:
- (a)$-1 < x < 1$
- (b)$-1 \le x \le 1$
- (c)$1 \le x < \infty$
- (d)$-\infty < x < -1$
Answer
Answer
Correct option: (a)
Answer: (a) $-1 < x < 1$
$f'(x) = 3x^2 - 3 = 3(x-1)(x+1) < 0$ exactly when $-1 < x < 1$, so $f$ is strictly decreasing there.