Question

Use differentials to approximate (3.98)^4. How?

Answer 1

well, a linear approximation might help

Answer 2

Here's an idea... start with
\[\huge y = f(x) = x^4\]

Answer 3

say

y = (x+c)^4

y' = 4(x+c)^3

Answer 4

y = y'(x+c) - y(c) is a linear approximation

Answer 5

\[\huge \frac{dy}{dx}=4x^3\]\[\huge dy = 4x^3 dx\]