What is the equation of the normal line of #f(x)=2x^3-x^2-3x+9# at #x=-1#?
Let's first find what point the tangent passes through, given
Therefore, the tangent passes through
Now that we know this, we must differentiate the function.
By the power rule:
The slope of the tangent is given by evaluating
The slope of the tangent is
This means the slope of the normal line is
Hopefully this helps!