Question

Use linear approximation, i.e. the tangent line, to approximate the square root of 49.2 as follows:
Let f(x)=x. The equation of the tangent line to f(x) at x=49 can be written in the form y=mx+b where
m = ?
b = ?

Answer 1

49 + (x-49) = x
m = 1
b = 0

Answer 2

I'm sorry that was my bad. The question actually is:
Use linear approximation, i.e. the tangent line, to approximate the square root of 49.2 as follows:
Let f(x)= the square root of x. The equation of the tangent line to f(x) at x=49 can be written in the form y=mx+b where
m = ?
b = ?

Answer 3

f(a) + f'(a) (x-a)

In this case, a = 49

Answer 4

Ok... So then what do I do?

Answer 5

what is the derivative of square root (x) ?

Answer 6

1 / (2 * square root(x))

Answer 7

square root (7) = plus / minus 7

Answer 8

\[\pm 7 + \frac{1}{\pm 14} (x-49)\]

Answer 9

Okay so what am I supposed to do next?

Answer 10

\[m = \frac{1}{\pm 14}\]

Answer 11

Got it :)
There's one more part to the problem, it says:
Using this (the answers from the previous parts), we find our approximation for square root (49.2) = ?

Answer 12

It also says: NOTE: For this part, give your answer to at least 9 significant figures or use fractions to give the exact answer.

Answer 13

plug in 49.2 for x