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

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Answer 1 · 2016-08-24T19:48:23

The linearization is the equation of the tangent line.

$f(x) = sqrt x$ , 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

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

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