My First Ever Self Made Calculus - Probability Question

Calculus Level 5

$\large f(x) = \cfrac{x^4}{4} - \cfrac{2x^3}{3} - \cfrac{5x^2}{2} + 6x + 69 \ , \ x \in [-10 , 10]$ For $$f(x)$$ as defined above, let $$A$$ be the largest local maximum point and $$B$$, the smallest local minimum point. If you choose a random real number $$z$$ in the interval $$[ -10, 10 ]$$, what is the probability that the point $$\big(z \ , \ f(z)\big)$$ lie on the curve $$AB$$?

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