Question

f(x)=x−9/(7x+2).
Find an equation for the tangent line to the graph of f at x=11.
Tangent line: y =

Answer 1

where are you stuck at ?

Answer 2

in the begining

Answer 3

what have you tried

Answer 4

what do you need to write an equation of line ?

Answer 5

i don't know how to do it !

Answer 6

equation of line with slope \(\color{red}{m}\) and y intercept \(\color{red}{b}\) :\[y = \color{red}{m}x + \color{red}{b}\]

Answer 7

thats called slope-intercept form of line, seen that before ?

Answer 8

yep

Answer 9

good, calculus gives you slope \(\color{red}{m}\) of that tangent line

Answer 10

f(x)=(x-9)/(7x+2)

Answer 11

\[f(x)=\dfrac{x-9}{7x+2}\]

like this ?

Answer 12

yep

Answer 13

Alright, here is the juicy formula
\[\text{slope} = \dfrac{d}{dx} f(x) \]

*read it like below :
slope of tangent line at x=11 is same as the derivative of function at x = 11

Answer 14

for slope, you find the derivative of f(x) and evaluate it at x=11

Answer 15

can you find the derivative of f(x) ?