Unit 4 - Objective 5 - Differentials

The differentials are the change in the variables along the tangent line.

For y = f (x) dx = x = Differential of independent variable dx = f ' (x) dx = Differential of dependent variable

Problem 1:	Foy y = 3x² - 7x + 2 find dy y = f (x), so dy = f' dx = (6x - 7) dx
Problem 2:
Problem 3:
Problem 4:

Differentials are used to approximate the change in the dependent variable.

If y = f(x), and the change in x, x, is "small", then the actual change in y = y is approximately equal to dy, the differential.

Use the differential to approximate the change in A = r² when r = 2 cm and r = 0.5 cm

Solution: Here A is function of r, A = f (r) so dA = f' (r) dr = f '(r) r

A dA = 2 r r	Now substitute in the values
2(2)(0.5) = 2 cm² 6.28 cm²l