Question

To estimate the numerical value of the square root of a number, we use a tangent line approximation about x = a. From the graph of √x, attached inside, decide for which number the error in using this approximation has the smallest magnitude.

A. √4.2 about x=4

B. √4.5 about x=4

C. √9.2 about x=9

D. √9.5 about x=9

E. √16.2 about x=16

F. √16.5 about x=16

Please explain? Thank you:)

Answer 1

the graph:)

Answer 2

:c ugh

Answer 3

Ugh?!? This is a wonderful problem!

Answer 4

hahaha :P

Answer 5

i would agree... if i knew how to solve haha

but i'll probably agree that it's an awesome problem when i understand it :P

Answer 6

Ugh as in its hard ha

Answer 7

Use differentials. First find the derivative of y = √x

Answer 8

If you look at the graph, you can see it seems to be "flattening" out a bit
that means as x gets bigger, the slope of the curve is getting smaller

If the slope of the curve is not changing quickly, then the tangent line will stay close to the curve.

Answer 9

derivative of √x = 1/2√x right?

Answer 10

@phi
yes i see that:)

so for this problem, we're looking for the smallest magnitude.. so would that be the part with the smallest slope?

Answer 11

the further you move to the right, the flatter the curve... the tangent will stay closer to the curve as you move your point to the right. Or, more obviously, if you are near the left side of the curve, the tangent does not match as well (it diverges from the curve)