Question

How do you find the linearization at x=2 of `f(x) = 3x - 2/x^2`?

Answer 1

Taylor: `11/2 + 13/4(x - 2) + O(x-2)^2`

Explanation:

`f'(x) = 3 + 2/x^3 => f'(2) = 3 + 2/8 = 13/4`

`L(x) = 13/4x + b and L(2) = f(2)`

`f(2) = 6 - 2/4 = 11/2`

`13/4 * 2 + b = 11/2 => b = 1`

The tangent line at x = 2 is `L(x) = 13/4 x + 1`