Warm up problem 1

Calculus Level 3

If you are just waking up or just got on brilliant, here is a great problem to warm up your mind with. I am beginning a new set of problems that will be titled "warm up problems". In this set, I will be posting about 1-2 mainly easy to medium level problems to warm up with. Hope you enjoy!

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

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