What is the equation of the tangent line of #f(x) =(x^2)/(x-4)# at #x=5#?

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Answer 1 · 2016-04-22T21:37:56

#y-25=-15(x-5)#

First, find the value of f(x) at x=5.

#f(5)=(5)^2/(5-4)=25#

Now, let's find the derivative of f(x) at x=5.

#d/dx(x^2/(x-4))=((2x)(x-4)-x^2)/(x-4)^2=f'(x)#

#f'(5)=((10)(1)-25)/(1)^2=-15#

With all this information, we can set up a tangent line equation for x=5. Here is the answer.

#y-25=-15(x-5)#