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Math 1220 Quiz 1 September 1, 2015 Answer the 3 questions below. The value of each question is indicated at the beginning of it. Please justify your answer in the space provided: writing the solution without any explanation might not be enough. You can use the homework exercises that you will be turning in today. Name: UID: 1. (6 pts) Compute the integral Z 0 1 t+1 dt 2t2 + 4t + 3 2. (6 pts) Compute the derivative of the function f (x) = x3 − ln(1 + ex ) e−2x − x 3. Consider the function Z x f (x) = 2 e−t dt 0 (a) (3 pts) What is the domain of f ? (b) (5 pts) Find f 0 (x) and determine where is f (x) increasing / decreasing. Are there any extreme points? (c) (5 pts) Find f 00 (x) and determine where is f (x) concave up / down. Are there any inflection points? Page 2