To solve this problem you must apply the proccedure shown below:
1. You have that
and
, therefore, you must divide must fucntion, as following:

2. You must simplify it,by factoring out
, as following:

3. Finally, you obtain that the answer is:

The answer is both a and b, but I think you meant to switch the greater/less signs, so then it would be x > 0.
Answer:
(-∞, -2) and (2, ∞)
Step-by-step explanation:
ƒ(x) = x³ -12x + 10
f'(x) = 3x² - 12
Set 3x² - 12 = 0
x² - 4 = 0
x² = 4
x = ±2
The points x = -2 and x = + 2 divide the number line into three intervals:
(-∞, -2), (-2, +2), and (+2, ∞).
a. Interval (-∞, -2)
x < -2, so f'(x) > 0 when -∞ < x < -2
The function is increasing in (-∞, -2).
b. Interval (-2, 2)
|x| < 2, so f'(x) <0
The function is decreasing in (-2, 2).
c. Interval (2, ∞)
x > 2, so f'(x) > 0 when 2 < x < ∞
The function is increasing in (2, ∞).
Thus, the function is increasing in the intervals (-∞, -2) and (2, ∞).
The rate of temperature rise is 2 degrees/minute.
The relation between temperature and time is of the form
y = 2x + b
where
x = time, minutes,
y = temperature, Celsius
When x = -4 min, y = - 4°C because the temperature was - 4°C 4 minutes ago. Currently, x = 0.
Therefore
-4 = 2(-4) + b
-4 = - 8 + b
4 = b
Part A
The relation is y = 2x + 4
Part B
When x = 15 (15 minutes from now), the temperature will be
y = 2(15) + 4 = 34°C
Answer: 34°C