Answer:
y = x+1
Step-by-step explanation:
The slope of the tangent line is the value of the derivative at the given point:
y' = 2(1/2x^(-1/2)) = 1/√x
For x=1, this value is ...
y' = 1/√1 = 1
The point-slope form of the equation for a line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
For m = 1 and (h, k) = (1, 2) the equation of the line is ...
y -2 = 1(x -1)
y -2 = x -1 . . . . point-slope equation, simplified a bit
y = x +1 . . . . add 2 to get slope-intercept form
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Additional comment
We used the "power rule" for finding the derivative. That rule tells you ...
for y = x^a, the derivative is y' = a(x^(a-1))
In this problem, the exponent 'a' is 1/2, so (a-1) is -1/2.
