Consider the function and its derivative: g(x)= 57:2/3 _ 275/3 2(x2 - 10) (x - 2)2 d'(x) = = 3Vx(x - 2)3 a) Find the critical numbers. b) Find the intervals of increase and decrease for g by using a sign chart. c) Use the first derivative test to determine the local extrema and find their locations. Explain what is happening at each critical point and use your analytical work to support your answer. Your solution should show your understanding of . finding critical numbers analytically . creating and using a sign chart; completing a sign chart by hand with a calculator for com- putation . using the first derivative test and finding the location of local extrema