Silhouette of a Fish

Calculus Level 3

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

16y2=a+15x9x2+x316y^2=a+15 x-9 x^2+x^3

Note: bb is a constant of real integral value.

Image Credit: Flickr Larry
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