高数 求出 然后怎么做
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高数
![](http://img.wesiedu.com/upload/4/dd/4ddcc4d46205201c48b853c916309e49.jpg)
求出
然后怎么做
![](http://img.wesiedu.com/upload/4/dd/4ddcc4d46205201c48b853c916309e49.jpg)
求出
![](http://img.wesiedu.com/upload/8/a9/8a93b3e0c4a1142e318eba84006b247d.jpg)
![高数 求出 然后怎么做](/uploads/image/z/18380153-65-3.jpg?t=%E9%AB%98%E6%95%B0+%E6%B1%82%E5%87%BA%26nbsp%3B%E7%84%B6%E5%90%8E%E6%80%8E%E4%B9%88%E5%81%9A%26nbsp%3B)
V=π∫(0,1)[3x²+cx]²dx
=π∫(0,1)(9x^4+6cx^3+c^2x^2)dx
=π(9/5x^5+3/2cx^4+1/3c^2x^3)|(0,1)
=π(9/5+3/2c+1/3c^2)
=π/30 (10c²+45c+54)
v'(c)=π/30(20c+45)=0
c=-45/20=-9/4
v''(c)>0
所以
当c=-9/4时取最小值.
=π∫(0,1)(9x^4+6cx^3+c^2x^2)dx
=π(9/5x^5+3/2cx^4+1/3c^2x^3)|(0,1)
=π(9/5+3/2c+1/3c^2)
=π/30 (10c²+45c+54)
v'(c)=π/30(20c+45)=0
c=-45/20=-9/4
v''(c)>0
所以
当c=-9/4时取最小值.