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单选题 设 
与 
均为可微函数,且 
. 已知 
是 在约束条件 
下的一个极值点,下列选项正确的是( )
A. 若 
,则 
B. 若 
,则 
C. 若 
,则 
D. 若 
,则
学科：高等数学(理一2)
时间：2024-04-15 14:14:37
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题目1单选题
已知函数 <img src="https://tihai-oss-cloud.itihey.com/img/88b6b0686362ba2f7171419e4a47f460.png">在点 <img src="https://tihai-oss-cloud.itihey.com/img/5ec94b936d0f056fd86b249cc89d470c.png">的某邻域内连续,且 <img src="https://tihai-oss-cloud.itihey.com/img/d0e426cd506fd4f88ab28b5bd8cd6e41.png">其中 <img src="https://tihai-oss-cloud.itihey.com/img/a3ace43fe42611ad2c8d3f7cea306ab3.png">为非零常数,则 <img src="https://tihai-oss-cloud.itihey.com/img/f938922ea22247c2e433f20b83915c04.png">( )A. 是否取极值与 <img src="https://tihai-oss-cloud.itihey.com/img/a3ace43fe42611ad2c8d3f7cea306ab3.png">有关B. 是极小值C. 是极大值D. 不是极值
题目2单选题
设 <img src="https://tihai-oss-cloud.itihey.com/img/6785e28812d8a377f65b62a84f3202a9.png"> 则点 <img src="https://tihai-oss-cloud.itihey.com/img/8c1440821b1dd235b3c910907d46b40f.png">是该函数的()A. 驻点,且是极大值点B. 驻点,但不是极值点C. 偏导数不存在的点D. 驻点,且是极小值点
题目3单选题
设函数 <img src="https://tihai-oss-cloud.itihey.com/img/96ee10f45de88982f45a3b8d15c43d77.png">在点 <img src="https://tihai-oss-cloud.itihey.com/img/5499488bad46677b1ca2ab72754eb5b6.png">的某邻域内有连续的二阶偏导数,且 <img src="https://tihai-oss-cloud.itihey.com/img/9e708c82e31741578f0e70de342fcfe5.png">, <img src="https://tihai-oss-cloud.itihey.com/img/241a8536cac4df8887934383e74fbd2c.png">, <img src="https://tihai-oss-cloud.itihey.com/img/4d49fabd399271c9e89472594c4fbc01.png">, <img src="https://tihai-oss-cloud.itihey.com/img/a83635bdbf9adbaa4b1b5724279e87c5.png">,则在点 <img src="https://tihai-oss-cloud.itihey.com/img/5499488bad46677b1ca2ab72754eb5b6.png">的某邻域内,( )A. 由 <img src="https://tihai-oss-cloud.itihey.com/img/53f8576e9e95718e6be94131169c0f83.png">可确定函数 <img src="https://tihai-oss-cloud.itihey.com/img/be2ca3eda54c3fa663541ed4149f4410.png">,且 <img src="https://tihai-oss-cloud.itihey.com/img/be2ca3eda54c3fa663541ed4149f4410.png">在点 <img src="https://tihai-oss-cloud.itihey.com/img/a9545f7e60887de5c5ed3398dd8157ac.png">处取极大值B. 由 <img src="https://tihai-oss-cloud.itihey.com/img/53f8576e9e95718e6be94131169c0f83.png">可确定函数 <img src="https://tihai-oss-cloud.itihey.com/img/f80db68ac441c87b4c56d2ead73adaab.png">,且 <img src="https://tihai-oss-cloud.itihey.com/img/f80db68ac441c87b4c56d2ead73adaab.png">在点 <img src="https://tihai-oss-cloud.itihey.com/img/4496594bb6f791c6872c9ba04d2d3dab.png">处取极大值C. 由 <img src="https://tihai-oss-cloud.itihey.com/img/53f8576e9e95718e6be94131169c0f83.png">可确定函数 <img src="https://tihai-oss-cloud.itihey.com/img/be2ca3eda54c3fa663541ed4149f4410.png">,且 <img src="https://tihai-oss-cloud.itihey.com/img/be2ca3eda54c3fa663541ed4149f4410.png">在点 <img src="https://tihai-oss-cloud.itihey.com/img/a9545f7e60887de5c5ed3398dd8157ac.png">处取极小值D. 由 <img src="https://tihai-oss-cloud.itihey.com/img/53f8576e9e95718e6be94131169c0f83.png">可确定函数 <img src="https://tihai-oss-cloud.itihey.com/img/f80db68ac441c87b4c56d2ead73adaab.png">,且 <img src="https://tihai-oss-cloud.itihey.com/img/f80db68ac441c87b4c56d2ead73adaab.png">在点 <img src="https://tihai-oss-cloud.itihey.com/img/4496594bb6f791c6872c9ba04d2d3dab.png">处取极小值
题目4单选题
函数 <img src="https://tihai-oss-cloud.itihey.com/img/7ad28cd6eed70d2d204f4c46e0c0a5d8.png">在点 <img src="https://tihai-oss-cloud.itihey.com/img/97d2bfa2fd54fba1c41e4ed6125b09cd.png">处( )A. 取得极小值 <img src="https://tihai-oss-cloud.itihey.com/img/f6fa054daf68665fb96e8846d19f0d4e.png">B. 取得极小值 <img src="https://tihai-oss-cloud.itihey.com/img/daad39e286b0465c3a8a877b62632715.png">C. 不取得极值D. 取得极大值 <img src="https://tihai-oss-cloud.itihey.com/img/f6fa054daf68665fb96e8846d19f0d4e.png">
题目5单选题
设 <img src="https://tihai-oss-cloud.itihey.com/img/88b6b0686362ba2f7171419e4a47f460.png">与 <img src="https://tihai-oss-cloud.itihey.com/img/0fc24a577f8593ba97767aa905d29064.png">均为可微函数,且 <img src="https://tihai-oss-cloud.itihey.com/img/3964a81b9e7d1d6eae034f1e64fd31e1.png">. 已知 <img src="https://tihai-oss-cloud.itihey.com/img/013b92eb82bb5f24f26edfcd4758e12b.png">是 <img src="https://tihai-oss-cloud.itihey.com/img/88b6b0686362ba2f7171419e4a47f460.png">在约束条件 <img src="https://tihai-oss-cloud.itihey.com/img/ae561267123564c85644a834fb12e984.png">下的一个极值点,下列选项正确的是( )A. 若 <img src="https://tihai-oss-cloud.itihey.com/img/5929a844292a72ce6d9e936efa3472ed.png">,则 <img src="https://tihai-oss-cloud.itihey.com/img/3113110d3540d4f03b924e26950a3a89.png">B. 若 <img src="https://tihai-oss-cloud.itihey.com/img/5b9240bde989f35d503f043e311c2d74.png">,则 <img src="https://tihai-oss-cloud.itihey.com/img/7df86b9da0501804d2f6c302b2591c8a.png">C. 若 <img src="https://tihai-oss-cloud.itihey.com/img/cec4b31399d3ffcbc3f5b1c08fef7ed2.png">,则 <img src="https://tihai-oss-cloud.itihey.com/img/645520e17c66a8edaa2b629de5f33c2d.png">D. 若 <img src="https://tihai-oss-cloud.itihey.com/img/273176a67ae6177de1015e63fcc75a81.png">,则 <img src="https://tihai-oss-cloud.itihey.com/img/7df86b9da0501804d2f6c302b2591c8a.png">
题目6单选题
函数 <img src="https://tihai-oss-cloud.itihey.com/img/e79bdbee119a5f15195604dea8173c5b.png">( )A. 在点 <img src="https://tihai-oss-cloud.itihey.com/img/35f06e150269b7ec374cb40c9cca257e.png">处取极大值B. 在点 <img src="https://tihai-oss-cloud.itihey.com/img/47fc2418e76fd4742127c9f5e3d2362d.png">处取极小值C. 在点 <img src="https://tihai-oss-cloud.itihey.com/img/35f06e150269b7ec374cb40c9cca257e.png">处取极小值D. 在点 <img src="https://tihai-oss-cloud.itihey.com/img/47fc2418e76fd4742127c9f5e3d2362d.png">处取极大值
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