A piece of wire of lengh k cm is bent to form a sector. Find the maximum area od the sector.
麻煩llist D step丫
其實大概有個outline的step都得
一題Differentiation-optimization
2009-10-08 5:00 am
回答 (1)
2009-10-08 5:14 am
✔ 最佳答案
Let the radius of the sector be r cmLet the angle of the sector be θ radian
Perimeter = k = 2r + rθ
θ = (k - 2r) / r
Area of sector A = πr^2(θ /2π)
= r^2θ /2
= (r^2/2)(k - 2r)/r
= kr/2 - r^2
dA / dr = k/2 - 2r = 0
=> r = k/4
d^2A/dr^2 = - 2 < 0 => maximum
r = k/4
=> A = (k/2)(k/4) - (k/4)^2
=> A = k^2/16
Maximum area = k^2/16 cm^2
收錄日期: 2021-04-24 10:14:20
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