Question 1111345
derivative of x^3-3x^2+6x+3 is 3x^2-6x+6

The derivative is the slope of the line.  The minimum value is where x=-b/2a, like any quadratic.
That is x=6/6=1
The slope is 3-6+6 or 3. The point on the original function is (1, 7)

{{{graph(300,300,-10,10,-10,10,x^3-3x^2+6x+3,3x^2-6x+6)}}}