1 Problem 12 (2.1) from the textbook [10 points] Let f(x) = (x+2)(x+1)²x(x − 1)³ (x-2). To which zero of ƒ does the bisection method converge when applied on the following intervals? (a) [-1.5,2.5], (b) [-0.5, 2.4]. In your solution, please justify your answers. 2 Problem 14 (2.1) from the textbook [10 points] Find an approximation to √3 correct to within 10-4 using the Bisection Algorithm. You can use the code from the lecture, your own program, or just a calculator. Problem 18 (2.1) from the textbook [10 points] Use Theorem 2.1 to find a bound for the number of iterations needed to achieve an approximation with accuracy 10-3 to the solution of x3 + x − 4 = 0 lying in the interval [1,4]. 4 Problem 10 (2.2) from the textbook [10 points] Use Theorem 2.3 to show that g(x) = 2 has a unique fixed point on iteration to find an approximation to the fixed point accurate to within 10 5 Problem (exam question) [10 points] [,1]. Use fixed-point Let g(x) = 1 100 (sin(sin(x)) + x)+7. (a) Define the fixed point of g. (b) Prove that g has an unique fixed point in the interval [6.5, 7.5].

What does it mean to say that f(4) is a local maximum valueof f ?

Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f decreases on the interval -,x1 and increases on the interval x1,, then fx1 is a local maximum value.

What is the purpose of the Intermediate Value Theorem?