曲线f(x)根号下x分之1在x=1处的切线方程是?

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曲线f(x)根号下x分之1在x=1处的切线方程是?

曲线f(x)根号下x分之1在x=1处的切线方程是?
曲线f(x)根号下x分之1在x=1处的切线方程是?

曲线f(x)根号下x分之1在x=1处的切线方程是?
f(x) = √ (1/x)
f'(x) = (1/2)(1/x)^(-0.5) (-1/x^2)
f'(1) = -1/2
f(1) = 1
切线方程
(y-1)/(x-1) = -1/2
2(y-1) = -x +1
x+2y-3 = 0

y=x^(-1/2),
y'=(-1/2)x^(-3/2),
切点为(1,1),
y'(1,1)=-1/2,切线方程为:(y-1)/(x-1)=-1/2,
y=-x/2+3/2.

f(x)=(1/x)^(1/2)=x^(-1/2)
f '(x)=(-1/2)x(-3/2)
k=f'(1)=-1/2
f(1)=1
切线方程y-1=(-1/2)(x-1)
整理得x+2y-3=0