The image you provided contains several mathematical problems. Let's go through them one by one:

1. Determine the critical points, relative extrema, points of inflection, and other properties for the function: $f(x) = 5x^{2/3} - x^{5/3}$ We are asked to determine:

   • Critical points,
   • Relative extrema,
   • Points of inflection,
   • Intervals where the function is increasing or decreasing,
   • Concavity of the graph,
   • Slope of the inflectional tangent.

2. For a function $f$, differentiable on some open interval containing $c$, if $f''(c) > 0$, is the graph of $f$ concave upward at $(c, f(c))$? We need to explain why this is true.

3. Find the point on the curve $y^2 - x^2 = 1$ that is closest to the point $(2, 0)$.

4. Find the shortest distance from the point $M = (2, \frac{1}{2})$ to a point on the parabola $y = x^2$, and find the point on the parabola that is closest to $M$.

Would you like me to walk you through each problem step by step or focus on solving one problem in detail first?