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How would you explain a critical point? A minimum/maximum? a zero?

hmm i dont know haha... i know that i need to find the derivative first though.

So it sounds like you need to take the derivative, set it to zero and then solve for x.

and i got \[f'(x) = 5(x-2)^4(x+3)^4 + 4(x+3)^3(x-2)^5\]

embarrassing, but i honestly have no idea how to factor that. ha.

Well, the idea is to find an alternative to brute force.