Evaluate and compare Change in Y and Change in dy.
Y = 1-2X^2
To evaluate and compare the change in Y and the change in dy, we first need to find the derivative of the function Y = 1-2X^2.
To find the derivative, we can use the power rule. If we have a function of the form f(x) = ax^n, then the derivative is given by f'(x) = n * ax^(n-1).
Applying the power rule to the function Y = 1-2X^2, we find:
Y' = -4X
Now, let's evaluate the change in Y and the change in dy.
The change in Y represents the difference in Y values between two specific points on the function. It can be calculated by subtracting the Y value at one point from the Y value at another point. Let's consider two arbitrary points on the function, (x1, Y1) and (x2, Y2).
Change in Y = Y2 - Y1
The change in dy represents the difference in the derivative values between the same two points. It can be calculated in a similar way:
Change in dy = dy2 - dy1
Since the derivative of Y is Y' = -4X, we can evaluate the change in dy as:
Change in dy = (-4x2) - (-4x1) = -4(x2 - x1)
In summary, to evaluate and compare the change in Y and the change in dy for the function Y = 1-2X^2, we need to find the derivative and then calculate the differences in Y and dy values between two specific points on the function.