偶函数f(x)=ax4+b3+cx2+dx+e的图像经过(0,1),且在x=1处的切线方程y=x-2,求f(x)的解析式

f(x)图像经过(0,1)
f(x)=ax^4+bx^3+cx2+dx+1
f(x)是偶函数
f(x)=f(-x)
ax^4+bx3+cx2+dx+1=ax^4-bx^3+cx^2-dx+1
2bx3+2dx=0
b=0 d=0
f(x)=ax^4+cx2+1
f`(x)=4ax^3+2cx
f`(1)=4a+2c=1
f(1)=a+c+1
y=x-2a+c+1=1-2=-1
a+c=-2
a=5/2 c=-9/2
f(x)=5x^4/2-9x^2/2+1