Question

Find the derivative from the left at x = 2.
f(x)=sqrt(4-x^2)

Answer 1

have you got to the chain rule yet?

Answer 2

Not yet

Answer 3

damn

Answer 4

can't solve without chain rule?

Answer 5

so you have to compute
\[\lim_{x\to 2^-}\frac{\sqrt{4-x^2}}{x-2}\] i guess

Answer 6

multiply top and bottom by \(\sqrt{4-x^2}\) to get
\[\frac{4-x^2}{(x-2)\sqrt{4-x^2}}\] then factor and cancel

Answer 7

the denominator is still equal to 0, as I cancel (x-2)

Answer 8

What rules do you get to use?

Answer 9

Just the definition of a limit?

Answer 10

\[
\Large
\lim_{h\to 0^-}\frac{\sqrt{4-(x+h)^2}-\sqrt{4-x^2}}{h}
\]