Find the cubic function y = x^3 + ax^2 + b^x + c whose graph has a horizontal tangent at (-2, 10) and passes through (1,1).

What I tried so far is plugging in -2 and 1 in the original function to get:

-8 +4a -2b +c = 10

1 + a + b + c = 1

And I have y' = 3x^2 + 2ax + b, which when I plug in -2 I get

0 = 12 - 4a + b (so b = -12 + 4a), but I have no clue where to go from there..even though I have a feeling it's something easy.

So if someone could give me a hint as to where to go next, that would be great! thanks for your time