题目内容
曲线f(x)=
ex-f(0)x+
x2在点(1,f(1))处的切线方程为________.
y=ex-![]()
[解析] 依题意,得f′(x)=
ex-f(0)+x,f′(1)=
×e-f(0)+1,f(0)=1,f(0)=
-f(0)×0+
×02,即f′(1)=e,f(1)=
·e-f(0)+
=e-
,因此所求的切线方程是y-
=e(x-1),即y=ex-
.
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题目内容
曲线f(x)=
ex-f(0)x+
x2在点(1,f(1))处的切线方程为________.
y=ex-![]()
[解析] 依题意,得f′(x)=
ex-f(0)+x,f′(1)=
×e-f(0)+1,f(0)=1,f(0)=
-f(0)×0+
×02,即f′(1)=e,f(1)=
·e-f(0)+
=e-
,因此所求的切线方程是y-
=e(x-1),即y=ex-
.