F(x+y)=fx+fy+2xy f'(0)=2

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F(x+y)=fx+fy+2xyf''(0)=2F(x+y)=fx+fy+2xyf''(0)=2F(x+y)=fx+fy+2xyf''(0)=2f（x+y）=f(x)+f(y)+2xy对该式中x求偏导得：f

F(x+y)=fx+fy+2xy f'(0)=2
F(x+y)=fx+fy+2xy f'(0)=2

F(x+y)=fx+fy+2xy f'(0)=2
f（x+y）=f(x)+f(y)+2xy对该式中x求偏导得：f '(x+y)=f '(x)+2y
再令x=0得：f '(y)=2+2y
再积分得 F(y)=2y+y^2
即F(x)=2x+x^2

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