Question

How do you find the linearization of `f(x) = sqrt(x)` at x=49?

Answer 1

The linearization is the equation of the tangent line.

Explanation:

`f(x) = sqrt x`, so `f(49) = 7`

and `f'(x) = 1/(2sqrtx)`, so `f'(49) = 1/14`

The tangent line is

`y-7 = 1/14(x-49)`, so the linearization is

`l(x) = 7 + 1/14 (x-49)`