Did you know?
Did you know that calculating the tangent lines at the intersection points of the y-axis can be done using the equation x=4y-y^2? By substituting y=0 into the given equation, we can find the x-values of the intersection points on the y-axis. Once the x-values are obtained, we can differentiate the equation with respect to y to find the derivative dy/dx. Finally, by using the point-slope form of a line, y-y1=m(x-x1), with the x and y values of the intersection points and the slope dy/dx, we can determine the equations of the tangent lines at those points. This process allows us to study the behavior of the curve at the intersection points and better understand its characteristics.
