Question

What is the equation of the tangent line of `f(x)=(x^3-3x +1)(x+2)` at `x=1`?

Answer 1

The equation of the tangent line of f at x = 1 is y = -x - 2.

Explanation:

The general equation of the tangent line of a given function `f` at `a in I` where `I` is the part of `RR` where the function is defined is given by the formula : `y = f'(a)(x - a) + f(a)`. We're going to use it here.

You first need `f'`, which will instantly give you the coefficient of the variable.

`f'(x) = 3(x^2 - 1)(x + 2) - x^3 - 3x + 1`

You calculate `f'(1)` which equals to `-1`. You use the formula given above and you will find that `y = -x - 1` is the tangent you were looking for.