How do you find the equation of the tangent line to the graph of #f(x)=sqrt(x-1)# at point #(5,2)#?

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Answer 1 · 2017-07-02T21:03:51

#y=1/4x+3/4#

First, we need to find #f'(5)# which will give us the gradient of the tangent.

#f(x)=sqrt(x-1)=(x-1)^(1/2)#

#f'(x)=1/2(x-1)^(-1/2)=1/(2sqrt(x-1))#

#f'(5)=1/(2sqrt(5-1))=1/(2sqrt(4))=1/4#

#thereforem_("tan")=1/4#

Now use #y=m(x-x_1)+y_1# to find the equation of the tangent.

#y=1/4(x-5)+2#

#y=1/4x+3/4#