y= 3x^2+3x+2

Find the diferential dy when x=4 and dx = 0.4 and when dx = 0.8.

How do I find these diferentials?

y= 3x^2+3x+2
dy= 6x dx + 3dx

Now put in the values, and compute.

To find the differentials, you can use the formula:

dy = (dy/dx) * dx

In this case, the equation is y = 3x^2 + 3x + 2. Taking the derivative of y with respect to x, we get:

dy/dx = 6x + 3

Substituting this into the differential formula, we have:

dy = (6x + 3) * dx

Now, we can calculate the differentials when x = 4 and dx = 0.4 and when dx = 0.8:

1. When x = 4 and dx = 0.4:
dy = (6(4) + 3) * 0.4
= (24 + 3) * 0.4
= 27 * 0.4
= 10.8

2. When x = 4 and dx = 0.8:
dy = (6(4) + 3) * 0.8
= (24 + 3) * 0.8
= 27 * 0.8
= 21.6

Therefore, the differential dy is 10.8 when dx = 0.4, and 21.6 when dx = 0.8.