Question

How do you find the equation of the tangent line to the graph of the given function `f(x) = 3x^3-x+1`; at (-1,-1)?

Answer 1

First you need to find the derivative of your function:
`f'(x)=9x^2-1`

Now yoy evaluate the derivative in `x=-1`;
`f'(-1)=9-1=8`; this is the slope `m` of the tangent.

Finally you may use the general relationship:
`y-y_0=m(x-x_0)` to find the equation of the tangent:
`y+1=8(x+1)`
`y=8x+8-1`
`color(red)(y=8x+7)`