Project 1. Consider the function f(x) to answer the questions. x+a x

Project 1. Consider the function f (x) to answer the questions. rx + a x < 0 Isinx x 0 a) At what values of a is the function continuous? Justify your answer. b) At what values of a is the function differentiable? Justify your answer with limit notation. 2. Consider the given function and table. f(x) h(x) x f(x) f'(x) 3 -5 7 a) Determine the equation of the tangent line to the graph of f (x) at x = 1. b) Is f (x) continuous at x = 2? Justify your response. c) Use the intermediate value theorem to justify the existence of a zero on the interval [1 , 3]. d) Determine h'(3). 3. Consider the functions f (x) and h(x) with continuous second derivatives. Copyright 0 2022 Imagine Learning LLC Student Guide (continued) x 2 f(x) f' (x) -2 5