Question

Consider the graph defined by

http://www.webassign.net/cgi-bin/symimage.cgi?expr=y%20%3D%20%28x%20-%205%29%2F%28x%20-%206%29

(a) Use the definition of the derivative to find the slope of the tangent line to the graph at the point (7, 2).
slope =

(b) Find an equation of the tangent line to the graph at the point (7, 2).
y =

Answer 1

dont use the definition, cheat and use the quotient rule

Answer 2

ok eric cartman

Answer 3

lols

Answer 4

how do i reach these kids

Answer 5

ok you write it out myininaya lets see you write this in latex using the definition. i will wait...

Answer 6

i cant scan it in? :(

Answer 7

let me know when you get \[\frac{-1}{(x-6)^2}\]

Answer 8

no you have to use latex

Answer 9

\[\lim_{x \rightarrow 7}\frac{\frac{x-5}{x-6}-2}{x-7}=\lim_{x \rightarrow 7}}\frac{x-5-2(x-6)}{(x-6)(x-7)\]
=\[\lim_{x \rightarrow 7}\frac{x-5-2x+12}{(x-6)(x-7)}=\lim_{x \rightarrow 7}\frac{-x+7}{(x-6)(x-7)}=\lim_{x \rightarrow 7}\frac{-(x-7)}{(x-6)(x-7)}\]
\[\lim_{x \rightarrow 7}\frac{-1}{x-6}=\frac{-1}{7-6}=\frac{-1}{1}=-1\]

Answer 10

i cant do it

Answer 11

no some of got messed up :(

Answer 12

i am totally impressed

Answer 13

on the other hand i was trying to write a compound fraction because i was just trying to find the derivative, not the value at 7. good work!

Answer 14

:)

Answer 15

wow its gettin heated up in here

Answer 16

i will rewrite the top

Answer 17

myininaya is showing me up;(

Answer 18

hahaha whose the better mathematician?

Answer 19

\[\lim_{x \rightarrow 7}\frac{\frac{x-5}{x-6}-2}{x-7}=\lim_{x \rightarrow 7}\frac{x-6}{x-6}\frac{\frac{x-5}{x-6}-2}{x-7}=\lim_{x \rightarrow 7}\frac{x-5-2(x-6)}{(x-6)(x-7)}\]

Answer 20

satellite is way better than me

Answer 21

haha

Answer 22

\[lim_{h->0}\frac{\frac{x+h-5}{x+h-6}-\frac{x-5}{x-6}}{h}\]

Answer 23

how do you like dem apples?

Answer 24

so anyways we found the slope of the tangent line to be -1
so a tangent line has form y=mx+b just like any other line
we know m=-1
we also know a point on the line (7,2)
so we can find b
2=-1(7)+b
2=-7+b
2+7=b
9=b
so the equation is y=-x+9

Answer 25

very cute satellite

Answer 26

right. once you have m = -1 it is all gravy from there

Answer 27

haha sweet already worked it out. thanks guys

Answer 28

good!