Question

Let y=3x^2

Find the change in y, ∆y when x=4 and ∆x=0.2_____?
Find the differential dy when x=4 and dx=0.2______?

Answer 1

When x = 4, y = 3(4)^2 = 3(16) = 48


Now add on 0.2, to get x = 4.2 and y = 3(4.2)^2 = 3(17.64) = 52.92


Notice that y goes from 48 to 52.92.


So the change in y is 52.92 - 48 = 4.92


This means that ∆y = 4.92

Answer 2

How can I find the other one?

Answer 3

use the idea that


dy/dx = derivative of y with respect to x


So basically derive y = 3x^2 and you'll get something in the form


dy/dx = f(x), where f(x) is your derivative function


From there, plug in dx = 0.2 and solve for dy

Answer 4

Oh plug in x = 4 as well into the function when you plug in dx = 0.2