Question
Find the intervals in which the following functions are increasing or decreasing.
f(x) = 5x3 - 15x2 - 120x + 3.
f(x) = 5x3 - 15x2 - 120x + 3.
✓
Answer
f(x) = 5x3 - 15x2 - 120x + 3 f'(x) = 15x2 - 30x - 120 = 15(x2 - 2x - 8) = 15(x - 4)(x + 2) For f(x) to be increasing, we must have f'(x) > 0 ⇒ 15(x - 4)(x + 2) > 0 ⇒ (x - 4)(x + 2) > 0 [Since, 15 > 0, 15(x - 4)(x + 2) > 0 ⇒ (x - 4)(x + 2) > 0] ⇒ x < -2 or x > 4 $\Rightarrow\text{x}\in(-\infty,-2)\cup(4,\infty)$ So, f(x) is increasing on $\text{x}\in(-\infty,-2)\cap(4,\infty).$
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