Let f(x) = 3x^4 + 4x^3 - 12x^2 - 24x + 5, x E R ( element of all real numbers)

f'(x) = 12x^3 + 12x^2 - 24x - 24

Let f'(x) = 0

12x^3 + 12x^2 - 24x - 24 = 0

12[(x+1)(x^2-2)]=0

therefore x=-1 or x=sqrrt2 or x= -sqrrt 2

Here's when i am having trouble.

How do i pick an appropriate start and end point?

I constructed a table:

(x) -2 | -1| √1 | √2

f’(x) -24| 0| -24 | 0

Why am i getting incorrect values, shouldn't the point before -1 give me a positive tangent instead of a negative one?

Edit: Solved, thanks anyway.