# Thread: Equations and critical points

1. ## Equations and critical points

Hello, I'm working on curve sketching, relative maxima/minima, etc, and I'm having trouble with this question:

For the function f(x) = 3x^4 + ax^3 + bx^2 + cx + d

Find constants a, b, c, and d that guarantee that the graph of f will have horizontal tangents at (-2, -73) and (0, -9). Find the third point that has a horizontal tangent, and for all 3 points, determine whether each corresponds to a relative maximum or minimum.

The farthest I got in this was figuring that (x+2) and (x+0) must be factors of the derivative in order to be critical points. However, this doesn't get me very far, and I'm not sure where to go from there. Thank you in advance for any help!

2. Originally Posted by starswept
For the function f(x) = 3x^4 + ax^3 + bx^2 + cx + d

Find constants a, b, c, and d that guarantee that the graph of f will have horizontal tangents at (-2, -73) and (0, -9). Find the third point that has a horizontal tangent, and for all 3 points, determine whether each corresponds to a relative maximum or minimum.
Use the fact that f(0)=-9, f(-2)=-73, f'(0)=0 and f'(-2）=0.
Use the four equations too find the for unkown constants.