How do you find the equation of the tangent line to the curve #y= 4/(x-1)# at point of (0,-4)?

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Answer 1 · 2016-12-10T01:58:01

#y = -4x - 4#.

Differentiate using the quotient rule to find the instantaneous rate of change of the function at #x= 0#.

#y' = (0(x - 1) - 4(1))/(x - 1)^2#

#y' = -4/(x - 1)^2#

The instantaneous rate of change at #x = a# is given by #f'(a)#.

#m_"tangent" = -4/(0 - 1)^2#

#m_"tangent" = -4/1#

#m_"tangent" = -4#

The equation can now be obtained.

#y - y_1 = m(x - x_1)#

#y - (-4) = -4(x - 0)#

#y + 4 = -4x#

#y = -4x - 4#

Hopefully this helps!