The point $P(4 , 24 )$ lies on the curve $y = x^2 + x + 4$. If $Q$ is the point $(x, x^2 + x + 4 )$, 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 $P(4 , 24 )$.