Question

Find equations of the tangent line and normal line to the curve at the given point.

Answer 1

\[y=\frac{ \sqrt{x} }{ x+9 }\]

Answer 2

Given point (1,0.1)

Answer 3

first you nee to find the derivative y' . This will give you the slope of the line in terms of x.

Answer 4

\[\frac{(x+9)(\frac{ 1 }{ 2 } x ^{-1/2})-(x ^{1/2})(1)}{ (x+9)^2}\]

Answer 5

yes thats correct
now plug in x = 1 to find the numerical value of slope at the point (1,0.1)

Answer 6

1/2 * (1)^(-1/2) = 1/2 * 1 /1^ 1/2

Answer 7

= 1/2

Answer 8

is the slope 4/100?

Answer 9

right or 0.04

Answer 10

y-0.1=.04(x-1)

Answer 11

y=.04x-.04+0.1

Answer 12

yes thats the tangent

Answer 13

y=.04x+.06

Answer 14

no - i think you have the last number wrong

Answer 15

ohh

Answer 16

sorry you are right!! my bad arithmetic!

Answer 17

ok xD

Answer 18

Now the normal as a slope of -1 / 0.04

Answer 19

is the normal line perpendicular?

Answer 20

yes

Answer 21

y-.1=-25(x-1)

Answer 22

y=-25x+25+.1

Answer 23

y=-25x+25.1

Answer 24

right

Answer 25

Thank you so much! You were so helpful :)

Answer 26

yw

Answer 27

you did pretty well too!!

Answer 28

aw thanks :)