What is the equation of the line tangent to # f(x)=(-3x-1)(x+4) # at # x=-1 #?

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Answer 1 · 2015-12-06T20:10:37

#y=-7x-1#

Find #f'(-1)#, the slope of the tangent line at the point on the function where #x=-1#.

To find this point, find #f(-1)=(-3(-1)-1)(-1+4)=6#.

The point where the tangent line will intersect is #(-1,6)#.

Now, find the slope of the tangent line:

#f(x)=-3x^2-13x-4#

#f'(x)=-6x-13#

#f'(-1)=-7#

Therefore #-7# is the slope of the tangent line at the point #(-1,6)#.

Write in point-slope form:

#y-6=-7(x+1)#

In slope-intercept form:

#y=-7x-1#