Step-by-step explanation:
Lets start with the easiest part of this question - simply plugging in to get easier equations:
Something that now immedietly pops out is that many of the terms would cancel if we added them together. We get the following results by adding the two equations together:
Now lets look at the other bit of inromation the question gives you -- that the two points are horizontal tangents. Taking the derivative of the standard form of a cubic, we get:
Since the points are both horizontal tangents, y' will be equal to 0 at the points. Thus, plugging in we get:
We again see a simple subtracting opportunity that will cancel out two terms:
Now going back to the equation we got by adding the two equations that we got from simply plugging our points in:
Now that we have b and d, we can now plug them back into our step one and derivative equations in order to get a simple system:
Solving for a and c, we get:
Thus, finally, our answer is:
Attached is desmos, which you can use to check.