Silhouette of a Fish

Calculus Level 4

Find the minimum possible value of $$|a|$$ such that the function below is continuous along the interval $$[b,\infty)$$ and there is no value of $$x<b$$ such that $$y$$ is a real number.

$16y^2=a+15 x-9 x^2+x^3$

Note: $$b$$ is a constant of real integral value.

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