Problem 13b from Friday

Above is the solution to problem 13b on page 88. I realized my mistake soon after class. I was in too much of a hurry to think what the question was actually posing. There are two and only two solutions for the standard absolute value equation (abs(x)). If x is positive, abs(x) has the equation y = x. The slope of the tangent line for any positive x on abs(x) is 1. If x is negative, abs(x) has the equation y = -x. The slope of the tangent line for any negative x on abs(x) is -1. This is shown above when x = -3. The relationship mentioned previously is the reason for the negative sign outside the parentheses in the second step. The rest of the steps are sequential and should be easy to follow. I apologize for the mistake and I will apologize in advance for any future ones. Obviously, I am human and that is a general flaw for all of humanity. I will try to minimize it as much as I can as far as calculus goes.