Calculus problem

Question

Let y = 2x^2 + 3x + 2

Find the differential dy when x = 2 and dx = 0.2 ______________

Find the differential dy when x = 2 and dx = 0.4 ______________

Answer 1

Given f(x) = y = 2x² + 3x + 2

dy/dx = 4x + 3

But let's treat dy and dx as "small numbers" so...

dy = (4x + 3)*dx = 4x*dx + 3*dx

Given x = 2 --> y = 2(2)² + 3(2) + 2 => y = 16

Given dx = 0.2 ...

therefore dy = 4*(2)*0.2 + 3*0.2 = 1.6 + 0.6 = 2.2

Given dx = 0.4

therefor dy = 4*(2)*0.4 + 3*0.4 = 3.2 + 1.2 = 4.4