Find an equation of the tangent line to #y=x+ 2/x# at the point (2,3)?

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Answer 1 · 2018-05-23T22:29:18

#y=1/2x+2#

#f(x)=x+2/x# , #D_f=RR#*#=(-oo,0)uu(0,+oo)#

For #x!=0# we have

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

The equation of the tangent line at #M(2,f(2))# will be

#y-f(2)=f'(2)(x-2)# #<=>#

#y-3=(1-2/4)(x-2) #<=>#

#y-3=1/2(x-2)# #<=>#

#y=1/2x+2#

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