Find the intervals on which the given function is increasing and the intervals on which it is decreasing. f ( x ) = $-$ 2 x 2 $-$ 16 x $-$ 49
A) $\text { Increasing on } ( - \infty , - 4 ] \text { and decreasing on } [ - 4 , \infty )$ .
B) $\text { Increasing on } [ - 4 , \infty ) \text { and decreasing on } ( - \infty , - 4 ]$ .
C) $\text { No correct answer }$ .

Question

Quizplus · Accepted Answer

To find the intervals on which the given function is increasing or decreasing, we need to find its derivative and then determine where it is positive or negative. Taking the derivative of the given function: f'(x) = -4x - 16 Setting this equal to zero to find critical points: -4x - 16 = 0 -4(x+4) = 0 x = -4 Therefore, the critical point is x = -4. Now, we can use test points to determine the sign of the derivative and hence, the intervals of increase and decrease: For x < -4, choose x = -5 (any number less than -4 can be used) f'(-5) = -4(-5) - 16 = 4 > 0 Therefore, f(x) is increasing on ( - ∞,-4]. For x > -4, choose x = -3 (any number greater than -4 can be used) f'(-3) = -4(-3) - 16 = -28 < 0 Therefore, f(x) is decreasing on [-4,∞). Thus, the answer is A, increasing on ( - ∞,-4] and decreasing on [-4, ∞).

Find the Intervals on Which the Given Function Is Increasing −-−

Find the Intervals on Which the Given Function Is Increasing $-$