4 minus the cube of a number?
1 answer:
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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, ∞).
<h3>Answer: (3, -1)</h3>
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Explanation:
The midpoint formula is
This basically says to add the corresponding coordinates and divide by 2.
The given points (2,5) and (4,-7) have x coordinates of 2 and 4. They add to 2+4 = 6, and then that result cuts in half to 6/2 = 3. The x coordinate of the midpoint is 3.
The y coordinate of the midpoint is y = -1 since adding the y coordinates of the given points leads to 5+(-7) = -2 which cuts in half to -1.
So overall the midpoint is located at (3, -1)
For this case we have a function of the form:
Where,
A: initial population
b: growth rate
x: number of years.
We then have the following function:
For x = 4 years we have:
Answer:
the formula for exponential growth is:
y = 210000 * (1,125) ^ x
The population of Canyon Edge after 4 years is:
y = 336379
Where,
A: initial population
b: growth rate
x: number of years.
We then have the following function:
For x = 4 years we have:
Answer:
the formula for exponential growth is:
y = 210000 * (1,125) ^ x
The population of Canyon Edge after 4 years is:
y = 336379