Answer
slope$=13$
See graph.
Work Step by Step
1. Find the derivative of $f(x)=x^3+x$ as $f'(x)=3x^2+1$.
2. The slope of the tangent line is the same as the derivative at $x=2$, we have $m=3(2)^2+1=13$
3. The tangent line is $y-10=13(x-2)$ or $y=13x-16$
4. See graph.