Observation is needed

Calculus Level 4

Let ff be a continuous and differentiable function in (x1,x2)(x_1,x_2). And the following conditions hold for it: {f(x) f(x)x 1((f(x))4limxx1+((f(x))2=1limxx2((f(x))2=12\begin{cases} f(x) \ f'(x) \geq x \ \sqrt{1-((f(x))^4} \\ \displaystyle \lim_{x \to x_1^+} ((f(x))^2=1 \\ \displaystyle \lim_{x \to x_2^-} ((f(x))^2=\frac{1}{2} \end{cases}

Find the minimum value of (x12x22)(x_1^2-x_2^2)

Note : f(x)=df(x)dxf'(x)=\dfrac{df(x)}{dx}

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