The problem asks: Find the linearization of $f(x)= \sqrt{a+bx} $ at $0$
To get all parts of $L(x) \approx f(c) - f'(c)(x-c)$
I've done:
$$f(0) = \sqrt{a}$$ $$f'(0) = {b\over 2\sqrt{a}} $$
Now: $$L \approx \sqrt{a} + {b\over 2\sqrt{a}}(x-0)$$ $$= \sqrt{a} + {bx\over 2\sqrt{a}}$$
If I plug in $0$ I'm left with $\sqrt{a}$ however, I'm getting the wrong answer. What have I done wrong?
