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Answer :
The most appropriate choice of slope of a curve will be given by
Slope of the curve at x = 1.2 = -25
First option is correct
What is slope of a curve?
Slope of curve at a point is the tan of the angle that the tangent to the curve at that point makes with the positive direction of x axis.
Here,
f(x) = [tex]\frac{1}{x - 1}[/tex]
[tex]f^{'}(x) = \frac{d}{dx} (\frac{1}{x-1})[/tex]
= [tex]-(x -1)^{-2}[/tex]
= [tex]-\frac{1}{(x-1)^2}[/tex]
At x = 1.2,
Slope = [tex]f^{'}(1.2) = -\frac{1}{(1.2 - 1)^2}[/tex]
= -[tex]\frac{1}{0.04}[/tex]
= -25
First option is correct
To learn more about slope of a curve refer to the link:
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