Let on the interval

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let

m(x)=\ln x

on the interval

[1,e^{4}]

. Find the unique number

c

(1,e^{4})

whose tangent line is parallel to the line through the points

(1,m(1))

and

(e^{4},m(e^{4}))

. State the value of

c

and, in one concise sentence, explain why this value is unique.