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Answer 1 · 2017-11-14T11:19:22

#( 4 , 13 )#

If we think of #f(x)=2x+5# being #y=2x+5#

and #g(x)=-x^2+10x-11# being #y=-x^2+10x-11#

Then #2x+5=-x^2+10x-11#

Solving this will give the point of intersection of both functions:

#2x+5=-x^2+10x-11#

#->=-x^2+8x-16=0#

#->=x^2-8x+16=0#

Factor:

#(x-4)^2=0=>x=4#

Plugging this into:

#y=2x+5#

#2(4)+5=13#

Coordinates of tangent:

#( 4 , 13 )#

Graph:

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