How do you find the equation of the tangent line to a derivative of a function #3x^2-12# at f'(1)?

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Answer 1 · 2015-06-12T00:18:25

You're halfway there.

The Linear Approximation Method is:
#f_T(x) = f(a) + f'(a)(x-a)#

#= f(1) + f'(1)(x-1)#

#= (3x^2 - 12) + (6x)(x-1)#
at #x = 1# (except for the #x# on the far right)

#= (3(1)^2 - 12) + (6(1))(x-1)#

#= -9 + 6(x-1)#

#= -9 + 6x- 6#

#f_T(x) = 6x - 15#

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