The point P(4, 23) lies on the curve y=x^{2} +x+3[/tex] . If Q is the point (x, + x + 3), find the slope of the secant line PQ for the following values of x.

If x = 4.1, the slope of PQ is: ?

and if x=4.01, the slope of PQ is: ?

and if x=3.9, the slope of PQ is: ?

and if x= 3.99, the slope of PQ is:?

Based on the above results, guess the slope of the tangent line to the curve at P(4,23) ?

There is 5 questions. Please only answer if you have all of them. It is much much appreciated.