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OpenStudy (anonymous):

Find the slope of the tangent line to the curve f(x)= x^2 + x - 1/x at x=-2

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OpenStudy (anonymous):

You need to take the derivative of f(x) which represents you're curve. This will give you the slope as a function of x, and then you can plug in you're x value.

OpenStudy (anonymous):

that is \[f'(x)=2x+1+\frac{1}{x^2}\] now plug in -2

OpenStudy (anonymous):

you get \[f'(-2)=2\times -2+1+\frac{1}{(-2)^2}\]

OpenStudy (anonymous):

i get \[-\frac{11}{4}\] as the slope

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