jmc

Find the largest $x$-value at which the graphs of $f(x)=e^{3x^2-|\lfloor x\rfloor |!}+\left(\genfrac{}{}{0ex}{}{22+735235|\lfloor x\rfloor |}{2356}\right)+\varphi (|\lfloor x\rfloor |+1)+72x^4+3x^3-6x^2+2x+1$ and $g(x)=e^{3x^2-|\lfloor x\rfloor |!}+\left(\genfrac{}{}{0ex}{}{22+735235|\lfloor x\rfloor |}{2356}\right)+\varphi (|\lfloor x\rfloor |+1)+72x^4+4x^3-11x^2-6x+13$ intersect, where $\lfloor x\rfloor$ denotes the floor function of $x$, and $\varphi (n)$ denotes the sum of the positive integers $\le$ and relatively prime to $n$.