answers with no supporting work will receive no credit you are allowed to use your textbook your notes and your calculator 1

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1)Determine whether Rolle’s Theorem applies to the following function on the given interval. If so, find the point(s) guaranteed to exist by Rolle’s Theorem.


LaTeX: fleft(xright)=sinleft(2xright):;:left[0,frac{pi}{2}right]


2)Given the function LaTeX: fleft(xright)=3x-x^3


a) Find the critical values and intervals of increase and decrease.

b) Find the inflection points and intervals of concave up and down.

c) Sketch the graph. Be sure to label all points clearly on the graph.