Answer
$y=-2x+3 $
Work Step by Step
1. The tangent line at x=a passes through the point (a, f(a))$\\$
(we must first find f(a)$\\$
2. It has slope m$=f^{\prime}(a)\\$
3. Its equation (point slope): $y-f(a)=f^{\prime}(a)(x-a)\\$
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1. $x=1, \ \ \ f(1)$=$\displaystyle \frac{1}{1^{2}}=1.\\$
The point on the graph is $(1,1).\\$
2. Slope. $\\$
$f^{\prime}(x)=$ (power rule)$ = [x^{-2}]^{\prime}=-2x^{-3}\\$
$m=f^{\prime}(1)=-2(1)^{-3}=-2(1)=-2\\$
3. Equation. P$(1,1),\ m=-2 \\$
$y-1=-2(x-1) \\$
$y-1=-2x+2 \\$
$y=-2x+3 $
image enclosed: graph
