What is the equation of the line tangent to # f(x)=(3x-1)(2x+4) # at # x=-1 #?

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Answer 1 · 2015-12-01T01:47:15

#y=-2x-10#

Find #f'(-1)# for the slope of the tangent line at the point #(-1,-8)#.

#f(x)=6x^2+10x-4#

Recall that #d/dx[x^n]=nx^(n-1)#.

#f'(x)=12x+10#

#f'(-1)=-2#

We can use point-slope form to write the equation of the tangent line:

#y+8=-2(x+1)#

In slope-intercept form:

#y=-2x-10#