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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