Let $f(x)=x^2+x+7.$ Find the slope of the secant line from $x=4$ to each of the following $x$ values:

From $x=4$ to $x=3\mathrm{.}9$ :

From $x=4$ to $x=3\mathrm{.}99$ :

From $x=4$ to $x=3\mathrm{.}999$:

From $x=4$ to $x=4\mathrm{.}1$:

From $x=4$ to $x=4\mathrm{.}01$:

From $x=4$ to $x=4\mathrm{.}001$ :

Based on the above results, estimate the slope of the tangent line to $f(x)$ at $(4,27).$