Lets see if i understood:Equate the derivative of the cubic to -2, and you may express c as a function of x.
Then, substitute for c into the cubic and find where this new function's derivative is equal to -2. You will get 2 x-values. One of these will allow you to then easily find c and d.
My teacher said that this is just an exercise concept.Yes, after substituting for c, then taking the derivative, you have found:
Now, equate this to -2, and you will have 2 roots, one of which allows you to find by substitution into the original cubic and tangent line the value of d (when you equate the two as they must have the same value where they touch) and then use the x-value also in your expression for c to find its value.