Consider the region enclosed by the lines ,

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

Problem

Consider the region

R(k)

enclosed by the lines

y=8-x

y=kx

, the

y

-axis, and the vertical line

x=k

, where

0<k<4

. Find the value of

k

that produces the largest possible area of

R(k)