Q1. 10 Points \text { Let } g(t)=\left(1-t^{2}\right)^{5}\left(t^{2}+2\right)^{6} Q1. 1 Question 1 Part (a) 2 Points Find g' (t) and express your final answer in simplified factored form. Q1. 2

Question 1 Part (b) 4 Points Find all of the critical point(s) of g(t) and create a sign analysis chart for g' (t) in order to determine the (open) intervals where g(t) is increasing and decreasing. Clearly state which intervals g(t) is increasing and decreasing on and give your answer using proper interval notation. Q1. 3 Question 1 Part (c) 4 Points Use the First Derivative Test to classify the critical point(s) of g(t)as local maximums,minimums, or neither.