Please explain in detail and have all theorems used written down.

Define F(8) = [, V1 -x'dx. Sketch the graph of F on the interval [-2, 2] indicating: . critical points . local maxima and minima . intervals on which F is increasing and decreasing . intervals on which F is concave up or down. You do not need to calculate the value of the function at any point. You may assume without proof that the cube root function v@ is continuous (although this follows directly from Question 7 of the first homework set) but you do need to refer precisely to any other theorems you are using