The graph of (for ) and the -axis enclose a region that is cut off on the right by…

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

Problem

The graph of

y=6-x^{2}

(for

x\ge 0

) and the

x

-axis enclose a region that is cut off on the right by the vertical line

x=k

, where

0<k<3

. For what value of

k

is the area of this region greatest?