Numerical Value Questions

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1.
Max volume of cylinder inscribed in sphere of radius R is:
2.
The tangent to y = x^3 - x at a point makes 45 degrees with x-axis. The point(s) are:
3.
f(x) = 2x^3 - 3x^2 - 12x + 5 on [-2, 4]. Global max is:
4.
If f(0) = -2, f(3) = 7, and |f'(x)| <= 3, is this consistent?
5.
f(x) = x^3 + ax is increasing for all x iff:

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