Show all supporting work for all problems. 1) Demonstrate Rolle's Theorem using f(x) = x sin(x) 2) Evaluate the following limit using L'Hopital's Rule. on the interval [0, x]. lim #1 3) Find the critical values for f (x) = (x - 1)3. 4) For what values of x is f (x) = x4 - 4x increasing? Decreasing?5) Find any inection points and intervals of concavity for f[x) = x3 5x1 + 3x+ 6. E) A charter bus company advertises a trip for a group as follows: At least EC- people must sign up. The cost when 20 participants sign up is $30 per person. The price will drop by $2 perticket for each person that signs up after 20. If the bus can accommodate 28 people. how many participants will maximize the company's revenue? 7') Given the graph of for) shown below. sketch a possible graph of x). You may sketch your answer on the same grid asf'tx}