Hi there!
We can find the values of x for which f(x) is decreasing by finding the derivative of f(x):
Taking the derivative gets:
Find the values for which f'(x) < 0 (less than 0, so f(x) decreasing):
0 = -8/x³ - 2
2 = -8/x³
2x³ = -8
x³ = -4
Another critical point is also where the graph has an asymptote (undefined), so at x = 0.
Plug in points into the equation for f'(x) on both sides of each x value to find the intervals for which the graph is less than 0:
f'(1) = -8/1 - 2 = -10 < 0
f'(-1) = -8/(-1) - 2 = 6 > 0
f'(-2) = -8/-8 - 2 = -1 < 0
Thus, the values of x are:
Answer:
5x^2 +10x
Step-by-step explanation:
The area is the product of the height and width. For this exercise, it is convenient to compute the rectangle areas individually, then write their sum:
blue rectangle area = (5x)(x) = 5x^2
red rectangle area = (5x)(2) = 10x
Total area = 5x^2 +10x.
_____
If you start by writing an expression for the total area, expanding it requires you deal with the unlike terms separately anyway:
5x(x +2) = 5x(x) +5x(2) = 5x^2 +10x
Answer:
19 > DB > 5
Step-by-step explanation:
In a triangle Δ ABC, AC = 7, and BC = 18.
Therefore, the length of the third side of the triangle Δ ABC i.e. length of AB can have a maximum value of < (7 + 18) i.e. 25 and the minimum value of the length AB will be > (18 - 7) i.e. 11
Hence, the length of AB will be given by 25 > AB > 11.
Now, AB = AD + DB = 6 + DB {Since length of AD is given to be 6}
Therefore, 25 > 6 + DB > 11
⇒ 19 > DB > 5 (Answer)
Answer:
- Point W = (-3, 3)
- Point X = (-3, 2)
- Point V = (-2, 3)
<em>The rotation rule states that rotation 90° counterclockwise means (x, y) = (-y, x)</em>
<u>The new points would be equal to:</u>
- Point W' = (-3, -3)
- Point X' = (-2, -3)
- Point V' = (-3, -2)
Try graphing it to see if the new points make sense<em>(because I'm not too sure :\)</em>