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单选题函数在点处沿向量的方向导数为( )

A. 6

B. 12

C. 2

D. 4

学科：高等数学

时间：2025-07-06 14:15:54

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设n 是曲面<img src="https://tihai-oss-cloud.itihey.com/img/4f94ea7168e3ee018bce3bbc0d48f9c8.webp"> 在点 P(1,1,1)处的指向外侧的法向量,求函数<img src="https://tihai-oss-cloud.itihey.com/img/c54bb4c674f7518302f7d4253cf0080c.webp"> 在点P 处沿方向n 的方向导数为( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/39a3de6638167a0458766b621c26c29f.webp">B. <img src="https://tihai-oss-cloud.itihey.com/img/16008f864bc2e473ba232fc44d783844.webp">C. <img src="https://tihai-oss-cloud.itihey.com/img/75ba749987fbf92c13856a80eb81ce87.webp">D. 2

在<img src="https://tihai-oss-cloud.itihey.com/img/fda3b33b20f466b7564f77198285fb38.webp">的某邻域内,<img src="https://tihai-oss-cloud.itihey.com/img/de9dd765d01194d69f72ec62bd0881a2.webp">存在是函数<img src="https://tihai-oss-cloud.itihey.com/img/c229d1f126ae313cb1edb9aca8709b86.webp">在点<img src="https://tihai-oss-cloud.itihey.com/img/fda3b33b20f466b7564f77198285fb38.webp">连续的( ) 【下册第19讲】

A. 无关条件B. 充分条件C. 必要条件D. 充分必要条件

设函数 <img src="https://tihai-oss-cloud.itihey.com/img/a2e31a9a4bcd926f82bb5f82ac3ed35a.webp">,则f(x,y)的驻点个数为( )

A. 4B. 2C. 3D. 5

在xoy平面上求一点,使它到平面直线x=0, y=0及x+2y-16=0的距离之平方和最小,则该点坐标为( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/c271488e1ce4f2eec1aa02524bad5a1d.webp">B. <img src="https://tihai-oss-cloud.itihey.com/img/1eb9c20295dc003805a2dad08ee6332e.webp">C. <img src="https://tihai-oss-cloud.itihey.com/img/741a5a8dd89d4f9ffa5f34af34b05701.webp">D. <img src="https://tihai-oss-cloud.itihey.com/img/93f20e0cac4e7feb9ef8c8e26542d0b4.webp">

函数<img src="https://tihai-oss-cloud.itihey.com/img/93c2b73038ed4738bb00b10e5c9dad11.webp"> 在点<img src="https://tihai-oss-cloud.itihey.com/img/1e2fe351aaf92d37eef9449097c94415.webp">处沿从点<img src="https://tihai-oss-cloud.itihey.com/img/1e2fe351aaf92d37eef9449097c94415.webp">到点<img src="https://tihai-oss-cloud.itihey.com/img/93e223f9cfabe0af4e31ee6913beee22.webp">的方向<img src="https://tihai-oss-cloud.itihey.com/img/73e0e6f52d35c46f0fc90f56aae83e58.webp">的方向导数为( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/c8c767277f94176e0d597b1694b7aff0.webp">B. <img src="https://tihai-oss-cloud.itihey.com/img/4acf2279c091b522d836cbaf14b3fccc.webp">C. <img src="https://tihai-oss-cloud.itihey.com/img/f7728366e168927f5644c2eb861256b0.webp">D. <img src="https://tihai-oss-cloud.itihey.com/img/1985eaeb8087824b39eb9af95ceb88c1.webp">

函数<img src="https://tihai-oss-cloud.itihey.com/img/14ebf1f27edd7cb3f8a9f88cb8e30a86.webp">在点<img src="https://tihai-oss-cloud.itihey.com/img/041a1c587f129c1816729e01e20710c5.webp">处沿向量<img src="https://tihai-oss-cloud.itihey.com/img/edde784fb6f0888981478df8dcd3341e.webp">的方向导数为( )

A. 6B. 12C. 2D. 4

设<img src="https://tihai-oss-cloud.itihey.com/img/fa648d490f82f812e17f8fef4e958f71.webp">,其中f(u)为可导函数,则<img src="https://tihai-oss-cloud.itihey.com/img/3ed334435c6c88f91cc30463d50d2968.webp">( ) 【下册第19讲】

A. <img src="https://tihai-oss-cloud.itihey.com/img/7b0b0942a9ce79b981e6f4f9fe4c16a6.webp">B. <img src="https://tihai-oss-cloud.itihey.com/img/860cac6ed4a786a71a1c25d3734f9309.webp">C. <img src="https://tihai-oss-cloud.itihey.com/img/d4f5a36164fa88af4e20c4aa127b3705.webp">D. <img src="https://tihai-oss-cloud.itihey.com/img/e14dd46e860580ec93cf86709384e68d.webp">

设<img src="https://tihai-oss-cloud.itihey.com/img/0ab90ee40938b28fb0524e715685fb57.webp">,则下列结正确论的是( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/47a51b36efc28bd49ac64bafab178469.webp">是<img src="https://tihai-oss-cloud.itihey.com/img/a2ee522bba2ba601cf06f631f632cc86.webp">的最大值点B. <img src="https://tihai-oss-cloud.itihey.com/img/47a51b36efc28bd49ac64bafab178469.webp">是<img src="https://tihai-oss-cloud.itihey.com/img/a2ee522bba2ba601cf06f631f632cc86.webp">的极大值点C. <img src="https://tihai-oss-cloud.itihey.com/img/47a51b36efc28bd49ac64bafab178469.webp">是<img src="https://tihai-oss-cloud.itihey.com/img/a2ee522bba2ba601cf06f631f632cc86.webp">的极值点D. <img src="https://tihai-oss-cloud.itihey.com/img/c6ee007bc41462babbac3ec86ffb4574.webp">是<img src="https://tihai-oss-cloud.itihey.com/img/e8b82b9a8ca9e2648407dbfbd30c368c.webp">的驻点

设<img src="https://tihai-oss-cloud.itihey.com/img/961e963f2089ac2132c3f96821f677dc.webp">,其中f具有二阶连续偏导数,则<img src="https://tihai-oss-cloud.itihey.com/img/160bc97803b5ecdd5dc80ea533da110b.webp">( ) 【下册第19讲】

A. <img src="https://tihai-oss-cloud.itihey.com/img/1742f8d6856cb567c7992d169b782cc6.webp">B. <img src="https://tihai-oss-cloud.itihey.com/img/3ee1a8bbe4e4a13cfe4ad87046859dba.webp">C. <img src="https://tihai-oss-cloud.itihey.com/img/ee9d341f64b4c390f9febc9c4a817950.webp">D. <img src="https://tihai-oss-cloud.itihey.com/img/1e50c189c0277b41ead032540cc04bbd.webp">

设<img src="https://tihai-oss-cloud.itihey.com/img/e22171e76c10c398d7392c02430f40c6.webp">是二元函数<img src="https://tihai-oss-cloud.itihey.com/img/d55285b599b8db67360077f7749a6fb6.webp">的驻点,则该函数在该点处( )

A. 有极大值或极小值B. 不一定有极值C. 一定有极小值D. 一定有极大值

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