Final answer:
To find the change in y, first evaluate y at x=1 to get 4. Then evaluate y at x=1+0.2 to get 5.76. Delta y, which is the change in y, is thus 5.76 - 4 = 1.76.
Step-by-step explanation:
The student is asking how to find the change in y (denoted as delta y) when x=1 and delta x is equal to 0.2, given the function y = 4x^2. To calculate the change in y, we need to evaluate the function at x and x + delta x, and then subtract the former from the latter.
First, we compute y at x=1:
y = 4(1)^2 = 4
Then, we calculate y at x=1+0.2=1.2:
y = 4(1.2)^2 = 4(1.44) = 5.76
The change in y, or delta y, is the difference of these two values:
delta y = 5.76 - 4 = 1.76.