How do you determine at which the graph of the function #y=x^2+1# has a horizontal tangent line?

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Answer 1 · 2018-01-02T19:28:15

See below.

Horizontal tangents have a gradient of zero, so if we find the first derivative and solve it for zero, we can identify where these lie:

#d/dx(x^2+1)=2x#

#f'(x)=0#

#2x=0=>x=0 #

So horizontal tangent at #x= 0#:

#y=(0)^2+1=1#

coordinates #( 0 ,1)#

Equation of tangent line:

#y-1=0(x-0)#

#y=1#

Graph:

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