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

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Answer 1 · 2016-05-06T16:09:33

#f(x)=-6x+3#

#f'(x)=3(x-1)^2-6x#

#f'(1)=3(1-1)^2-6(1)=-6#

#f(1)=(1-1)^3-3(1)^2=-3#

#f(x)=f(a)+f'(a)(x-a)#

#f(x)=-3+(-6)(x-1)#

#f(x)=-3-6x+6#

#f(x)=-6x+3#