设f（x)有二阶连续导数，f（π)=2，求f（0)。

设函数f(x)有二阶导数,<img src='https://img2.soutiyun.com/ask/2020-12-12/97664846212744.png' />求<img src='https://img2.soutiyun.com/ask/2020-12-12/976648472201016.png' />

设函数f(x)二阶连续可导,且f(0)=0,f'(0)=1,求<img src='https://img2.soutiyun.com/ask/2020-12-08/976282425721188.png' />

设函数f(x)在x=x₀处的二阶导数f&quot;(x₀)=0，则曲线y=f(x)在x=x₀处( )． (A)有拐点 (B)无拐点 (C)可能有拐点也可能没有拐点 (D)以上都不对

求函数z=f(u，x，y)，u=xe^y的<img src='https://img2.soutiyun.com/ask/2020-09-25/969881639212366.png' />，其中f具有二阶连续偏导数。

设函数f(x)和g(x)在[0,1]上有连续导数,且f(0)=0,f'(x)≥0,g'(x)≥0.证明:对任何a∈[0,1],都有 <img src='https://img2.soutiyun.com/ask/2020-12-13/97672399961901.png' />

求下列函数的二阶偏导数(其中f具有二阶连续偏导数): <img src='https://img2.soutiyun.com/ask/2021-01-02/978463370161912.png' />

设函数y=f(x)具有二阶导数，且f(x)＞0，f"(x)＞0，△x为自变量x在点x0处的增量，△y与dy分别为f(x)在点x0处对应的增量与微分，若△x＞0，则()． A．0＜dy＜△y B．0＜△y＜dy C．△y＜dy＜0 D．dy＜△y＜0

设函数f(u,v)在R²上具有二阶连续偏导数。证明:函数 <img src='https://img2.soutiyun.com/ask/2021-02-02/981107588858527.png' />

设f"(x)存在,求下列函数的二阶导数<img src='https://img2.soutiyun.com/ask/2020-11-10/973871310253584.png' />; (1) y=f(x²);(2)y=ln[f(x)].

设f(x)在[0,2]上连续,且f(x)+f(2-x)≠0,求 <img src='https://img2.soutiyun.com/ask/2020-12-09/976373200636763.png' />

设函数<img src='https://img2.soutiyun.com/ask/2020-08-18/96660742963403.png' />其中g(x)有二阶连续导函数，且g(0)=1. (1)确定a的值，使f(x)在点x=0处连续； (2)求f'(x)； (3)讨论f'(x)在点x=0处的连续性.

设函数f(x)有二阶导数,且f"(x)≠1.求由方程<img src='https://img2.soutiyun.com/ask/2020-12-12/976648440000174.png' />确定的隐函数y=y(x)的一、二阶导数.

设函数f(x,y)在(x0，y0)的某邻域内具有连续二阶偏导数，且<img src='https://img2.soutiyun.com/ask/2019-07-12/931776851413807.png' />，则<img src='https://img2.soutiyun.com/ask/2019-07-12/931776867607056.png' />()。 A.必为f(x,y)的极小值 B.必为f(x,y)的极大值 C.必为f(x,y)的极值 D.不一定是f(x,y)的极值

设f(x)在x=x₀的邻近有连续的二阶导数,证明 <img src='https://img2.soutiyun.com/ask/2020-10-28/972750844252307.png' />

设f(x)为<img src='https://img2.soutiyun.com/ask/2021-02-02/981112914240121.png' />上以2π为周期，且具有二阶连续导数的函数, 记 <img src='https://img2.soutiyun.com/ask/2021-02-02/981112923970678.png' /> <img src='https://img2.soutiyun.com/ask/2021-02-02/981112932118144.png' />

设f(x,y)具有连续偏导数,且满足<img src='https://img2.soutiyun.com/ask/2021-01-10/979124316503936.png' />求<img src='https://img2.soutiyun.com/ask/2021-01-10/979124324709406.png' />.

.设函数u=f(x,y,z)有连续偏导数，且<img src='https://img2.soutiyun.com/ask/2021-01-02/978463716012693.png' />是由<img src='https://img2.soutiyun.com/ask/2021-01-02/978463730334512.png' />所确定的隐函数，求du.

考虑下列修正的牛顿公式(单点Steffensen方法) <img src='https://img2.soutiyun.com/ask/2020-09-10/968583151416147.png' /> 设f(x)有二阶连续导数,<img src='https://img2.soutiyun.com/ask/2020-09-10/968583169623188.png' />试证明该方法是二阶收敛的.