Find the intervals on which the given function is increasing and the intervals on which it is decreasing. f ( x ) = x ² + 7 A) $\text { Increasing on } [ 0 , \infty ) \text { and decreasing on } ( - \infty , 0 ]$ . B) $\text { Increasing on } ( - \infty , 0 ] \text { and decreasing on } [ 0 , \infty )$ . C) $\text { No correct answer }$ .

Question

Quizplus · Accepted Answer

To find intervals of increasing and decreasing, we need to find the derivative of the function. f(x) = x² - 12x + 7 f'(x) = 2x - 12 For f'(x) > 0, we have x > 6. This implies the function is increasing on [6, ∞). For f'(x) < 0, we have x < 6. This implies the function is decreasing on (-∞, 6]. Therefore, the correct answer is A) Increasing on [0, ∞) and decreasing on (-∞, 0].

Find the Intervals on Which the Given Function Is Increasing Increasing on [0,∞) and decreasing on (−∞,0]\text { Increasing on } [ 0 , \infty ) \text { and decreasing on } ( - \infty , 0 ] Increasing on [0,∞) and decreasing on (−∞,0]

Find the Intervals on Which the Given Function Is Increasing $\text { Increasing on } [ 0 , \infty ) \text { and decreasing on } ( - \infty , 0 ]$