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

a.) Compute the slope of the secant line $PQ$ for the following values of $x .$

When $x= 4.1$ , the slope of $PQ$ is:
When $x= 4.01$ , the slope of $PQ$ is:
When $x= 3.9$ , the slope of $PQ$ is:
When $x= 3.99$ , the slope of $PQ$ is:

b.) Based on the above results, guess the slope of the tangent line to the curve at $P(4 , 24 )$.

Answer: