Question

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

Answer 1

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.

Answer 2

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

Answer 3

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

Answer 4

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