.
(C) Since .
;
when .
(B) See Figure N4−22. Replace the printed measurements of the radius
and height by 10 and 20, respectively. We are given here that and
that . Since , we have , so
.
Replace h by 8.
(D) . Since y′ = 0 if x = 1 and changes from negative to
positive as x increases through 1, x = 1 yields a minimum. Evaluate y at x
= 1.
(A) The domain of y is −∞ < x < ∞. The graph of y, which is
nonnegative, is symmetric to the y-axis. The inscribed rectangle has area
A = 2xe−x^2.
Thus , which is 0 when the positive value of x is . This
value of x yields maximum area. Evaluate A.
(B) See the figure. If we let m be the slope of the line, then its equation is
