Final answer:
The derivative of the function y=Cx^2-9y^7 is always positive, indicating that the function is always increasing. The open interval where this function is increasing is (-∞, ∞).
Step-by-step explanation:
To find the interval where the function y=Cx^2-9y^7 is increasing, we need to first find the derivative of the function. The derivative of a function gives us the rate of change of the function. It tells us how the function is changing at every point, and we can use it to determine where the function is increasing or decreasing.
The given function can be written as y=(Cx^2)/9y^7. So, let us find the derivative of this function. First, apply the power rule to get the derivative which gives: dy/dx=(2Cx)/9y^6. You will notice that this expression is always positive since x^2 is always positive for real numbers, regardless of the value of x, meaning the given function is increasing for all x. Therefore, the open interval over which the function y=Cx^2-9y^7 increases is (-∞, ∞).
Learn more about Increasing Interval