Final answer:
To evaluate dy when y = x³ - 2x² + 1, x = 2, and dx = 0.2, we need to find the derivative dy/dx and then substitute the given values.
Step-by-step explanation:
To evaluate dy when y = x³ - 2x² + 1, x = 2, and dx = 0.2, we need to find the derivative dy/dx and then substitute the given values.
1. Find the derivative of y = x³ - 2x² + 1. Differentiating each term separately, we get dy/dx = 3x² - 4x.
2. Substitute x = 2 and dx = 0.2 into the derivative:
dy = (3x² - 4x)dx
Substituting x = 2 and dx = 0.2, we have:
dy = (3(2)² - 4(2))(0.2)
dy = (3(4) - 8)(0.2)
dy = (12 - 8)(0.2)
dy = 4(0.2)
dy = 0.8