Good warm up problem

Calculus Level pending

In case you are just waking up or you just got on brilliant, here is a great problem to warm up your mind with. Also, I'm starting a new set of problems called "the warm ups problem sets." Made of Relatively easy or medium difficulty problems. I will be posting probably 1 or more per day.

The minimum value of \(\frac{x^4}{2}+\frac{2x^3}{3}-4x^2-8x+2000\) can be written as a/b for co-prime integers a,b. Find a+b.

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