Can you write a linear function that approximates the graph of the function f(x) = square root of x; near x=4?

Question

I don't quite understand how to do this, so can someone help me with this?

Answer 1

f'(x) = 1/square root of x
f'(x) = 1/sqrt(4)
f'(x) = 1/2

Answer 2

Yes, you can. The key to understanding it involves understanding the meaning of the words 'approximate' and 'near'. The function y=x/2 has -exactly- the same value as y=√x exactly at x=4. But, as x moves away from 4, the values of the 2 functions begin to differ. The question is how much do they differ, and how far from x=4 are they before they diverge by 'too much' (whatever that means)

HTH

Doug