Answer
$y=0.25x+1 $
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. $x=4, \ \ \ f(1)$=$\sqrt{4}=2.\\$
The point on the graph is $(4,2).\\$
2. Slope. $\\$
$f^{\prime}(x)=$ (power rule)$ = [x^{1/2}]^{\prime}=\displaystyle \frac{1}{2}x^{-1/2}=\frac{1}{2\sqrt{x}}\\$
$m=f^{\prime}(4)=\displaystyle \frac{1}{2\sqrt{4}}=\frac{1}{4}=0.25\\$
3. Equation. P$(4,2),\ m=0.25 \\$
$y-2=0.25(x-4) \\$
$y-2=0.25x-1 \\$
$y=0.25x+1 $
image enclosed: graph