What is the answer to this problem?
1 answer:
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First of all, a positive average rate of change means that the function is increasing, so the answer can only be A->B or B->C.
The average rate of change is defined as
i.e. as the ratio between the vertical and horizontal gain.
In order to go from point A to point B, you gain 1 unit horizontally and 5 units vertically. So, the average rate of change is 5/1=5.
In order to go from point B to point C, you gain 1 unit horizontally and 3 units vertically. So, the average rate of change is 3/1=3.
The statement "<span>The rate of change of y with respect to x is inversely proportional to y^4" can be written mathematically as dy/dx = k/y^4
To solve the differential equation, we use variable saparable method.
y^4 dy = kdx
Integrating both sides gives,
y^5 / 5 = kx + A
y^5 = 5kx + 5A = Bx + C; where B = 5k and C = 5A
![y= \sqrt[5]{Bx+C}](https://tex.z-dn.net/?f=y%3D%20%5Csqrt%5B5%5D%7BBx%2BC%7D%20)
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To solve the differential equation, we use variable saparable method.
y^4 dy = kdx
Integrating both sides gives,
y^5 / 5 = kx + A
y^5 = 5kx + 5A = Bx + C; where B = 5k and C = 5A