Question

Over what interval is the graph of f(x) = –(x + 8)2 – 1 decreasing?

Answer 1

The answer to this question would be A. (-8, ∞)
Hope the helps!

Answer 2

The given function f(x) is decreasing on the interval : (-8, +∞)

Explanation:

The function is given to be : f(x) = (x + 8)² - 1

To find the interval of decreasing, first find the critical points of the function f(x)

f(x) = (x + 8)² - 1

⇒ f'(x) = 2(x + 8)

Critical Point : x = -8

Now, Intervals are : (-∞ , -8) and (-8, +∞)

For the interval : (-∞ , -8)

f'(x) > 0 ⇒ f(x) is increasing on this interval.

For the interval : (-8, +∞)

f'(x) < 0 ⇒ f(x) is decreasing on this interval.

Hence, The given function f(x) is decreasing on the interval : (-8, +∞)