Question

Approximate the instantaneous rate of change for the function.
f(x)=square root of x at x=4

Answer 1

What sort of approximation?

Answer 2

All I know this is given for instantaneous rate of change
lim b->a f(b)-f(a)/b-a

Answer 3

That isn't an approximation though. That's the exact formula.

Answer 4

\[
\lim_{x\to 4}\frac{\sqrt x -\sqrt 4}{x-4}
\]

Answer 5

Multiply top and bottom by conjugate of numerator. Can you do that?

Answer 6

do you know how to take the derivative, or must you use lim b->a f(b)-f(a)/b-a ?

Answer 7

I am not sure how, but it looks I need to use lim b->a f(b)-f(a)/b-a

Answer 8

if you use the limit formula, it looks like this. Let a= 4, and b = x+h= 4+h
\[\lim_{h \rightarrow 0}\frac{ \sqrt{4+h }-\sqrt{4 }}{ (4+h)-4 }\]