Question

Use the information to evaluate and compare ∆y and dy.

y = x^3                                 x = 1                           ∆x = dx = 0.1

Answer 1

Step 1:

The function is .

Apply derivative on each side with respect to .

Apply power rule of derivatives :.

The differential function is

Step 2:

The differential function is

If changes by a small amount this will cause to change by a small amount .

Substitute  in differential function.

Hence, the value of is

Solution:

The value of is

The value of is