Did You Know what Actually is Point of Inflection ? (Part-1)

Calculus Level 3

Let f(x)=x46x2+5.f(x)=x^4-6x^2+5. If P(x0,y0)P(x_0,y_0) is a point such that y0>f(x0)y_0>f(x_0) and there are exactly two distinct tangents drawn to the curve y=f(x),y=f(x), what is the maximum value of y0?y_0?

Try : Part-2

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