微分rate of change 問題

Let H be the height of the cone ,
h and r be the height and the radius of the cylinder , thenh / (16 - r) = H / 16
h = (16 - r) H / 16So the curved surface area of the cylinder
s
= 2πrh
= 2πr (16 - r) H / 16
= (π/8) (16r - r²)H Set ds / dr = (π/8) (16 - 2r)H = 0
H = 0 (rejected) or r = 8.d²s / dr² = (π/8) (- 2)H < 0
∴ Maximum r = 8. If the right cylinder with its greatest curved surface area is insribed in a right circular cone of radius 16cm, the radius of the cylinder is 8 cm.

The problem is not related to rate of change.