The interval in which the function f(x) = x^{ | vedclass

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(C) Given function: $f(x) = x^{3} - 6x^{2} + 9x + 10$ Find the derivative: $f'(x) = 3x^{2} - 12x + 9$ Factor the derivative: $f'(x) = 3(x^{2} - 4x + 3

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$(-\infty, 1) \cup (3, \infty)$

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(C) Given function: $f(x) = x^{3} - 6x^{2} + 9x + 10$ Find the derivative: $f'(x) = 3x^{2} - 12x + 9$ Factor the derivative: $f'(x) = 3(x^{2} - 4x + 3) = 3(x - 1)(x - 3)$ For the function to be increasing,we require $f'(x) > 0$: $3(x - 1)(x - 3) > 0$ $(x - 1)(x - 3) > 0$ This inequality holds when $x  3$. Thus,the function is increasing on the interval $(-\infty, 1) \cup (3, \infty)$.

The interval in which the function $f(x) = x^{3} - 6x^{2} + 9x + 10$ is increasing is:

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