Final answer:
The change in y (Δy) is equal to 64 when x is equal to 4 and Δx is equal to 0.2. The differential dy is equal to 12.8.
Step-by-step explanation:
To find the change in y (Δy) when x is equal to 4 and Δx is equal to 0.2, we can use the derivative of y with respect to x. Given y' = 4x², we can substitute the values of x and Δx into the derivative:
y' = 4(4)² = 4(16) = 64.
Therefore, the change in y (Δy) is equal to 64 when x is equal to 4 and Δx is equal to 0.2.
To find the differential dy, we can use the derivative y' = 4x². The differential dy is given by dy = y' * dx. Substituting y' = 4x² and Δx = 0.2 into the differential formula:
dy = 4(4)² * 0.2 = 4(16) * 0.2 = 64 * 0.2 = 12.8.