The discussion centers on the process of linearizing functions using the small angle method, specifically addressing the treatment of constants. When linearizing a function like y = x^2 + 3, it is essential to retain the constant for accurate approximation at a specific point. The derivative provides the slope of the linear approximation, which in this case is 2x. For example, at x = 3, the slope is 6, and the linear approximation must pass through the point (3,12), resulting in the equation y = 6x - 6.
PREREQUISITESStudents and educators in mathematics, particularly those studying calculus and linear approximation techniques, as well as anyone seeking to deepen their understanding of function behavior and derivatives.
I see, thank you. I was just looking at the method of linearizing where you take the partial derivative of every variable and noticed that you wouldn't have any constants left doing this.BvU said:Hey guy, no.
The derivative gives you the slope of a linear approximation. (in this case 2x).
A constant is still needed for the approximation in a particular point; e.g. if x = 3 the slope is 6 and the line has to go through the point (3,12), so a linear approximation there is y = 6x - 6 (or, if you want: (y-12) = 6 (x-3) )