10.) for the natural logarithm function, determine the point on the curve where its associated tangent line passes through the origin as depicted in this diagram.

f(x)=lnx

y=f(x)

dy/dx= 1/x

tangent at (x,y) has slope 1/x

eqn of tangent is y = mx + c

since the tangent passes through origin, c=0

substitute y = lnx and m= 1/x to above eqn

lnx = 1

x=e

y=lne=1