What is the minimum value of a²x + b²y where xy = c² ?

For the following three (03) items:
Let $y=f(x)=\frac{x\sin ^{-1}x}{\sqrt{1-x^{2}}}+\ln \sqrt{1-x^{2}}.$

What is the slope of the tangent to the curve y = f(x) at x = 0.5

For the following two (02) items:
Consider the function $f(x)=1-\sqrt[3]{(x-1)^{2}}$

The function has

A wire of length 20 cm is to be bent into a rectangle. Which of the following statements is/are correct?

I. The rectangle of the largest area is the square.

II. It is possible to form a rectangle of an area of$ 27c m ^ 2$

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