What is the equation of the line tangent to #f(x)=x^2 -x-9 # at #x=-1#?

1 Answer
Mar 13, 2018

You have to use geometric derivative concept. See below

Explanation:

We know that the derivative #f´(x_0)# is the value of the slope of tangent line to #f(x)# in #x=x_o#

We have to do the derivative of #f(x)#

#f´(x)=2x-1# this function has the value in #x_0=-1#

#f´(-1)=2·(-1)-1=-3#

So the slope of tangent line to #f(x)# in #x_0=-1# is #-3#

Then the equation of tangent line has the form #y=-3x+b# where #b# is the intercept with #y# axis. Lets determine #b#

However #f(x)# and line are tangents in #x_0=-1# the value in both equations must be the same in #x_0=-1#.

#f(-1)=1+1-9=-7#
#y_(-1)=-3·(-1)+b=-7#. From here we can obtain #b# which is #b=-4#. Then the equation of tangent line to #f(x)# in #x_0=-1# is #y=-3x-4#