\fView an example | 5 parts remaining For y = f(x) = x" - 9x* + 5, find dy and Ay, given x = 5 and Ax = 0.1. First, recall the definition of the differential, dy, for the function y = f(x). dy = f'(x)dx Then, write an expression for the differential of y = f(x) = x# - 9x3 + 5. dy = f'(x)dx = (4x3 -27x2) dx. Now, recall that dx = Ax. Substitute x = 5 and Ax = 0.1 into dy = (4x3 - 27x2) dx. dy = (4(5)3 -27(5)2) 0.1 = - 17.5 Simplify. So dy = - 17.5.Next, calculate the change in y, Ay = f(x + Ax) -f(x). Substitute x = 5 and Ax = 0.1 into Ay. Ay = f(x + Ax) - f(x) = f(5 + 0.1) - f(5) = f(5.1) - f(5) Simplify the argument of the first term. = ((5.1)4 -9(5.1)3 +5) -f(5) Evaluate f(5.1). = - 512.3389 - f(5) Simplify. = - 512.3389 - ((5)4 -9(5)3 +5) Evaluate f(5). = - 512.3389 - (-495) Simplify. = - 17.3389 Simplify. For x = 5 and Ax = 0.1, we have Ay = - 17.3389 and dy = - 17.5