Consider the following function.

f(x) = x^1/3, a = 1, n = 3, 0.8 x 1.2

Consider the following function. f(x) = x1/3, a =1, n = 3, 0.8 x 1.2 (a) Approximate f by a Taylor polynomial with degree n at the number a. Ta(x) = 1+ (x - 1) (x- 1)2 5(x - 1) 3 3 9 81 (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) & 7 (x) when x lies in the given interval. (Round your answer to eight decimal places.) IR3(x)| 0.00015 X (c) Check your result in part (b) by graphing IR,, (x)1. y 0.00012 y 0.00010 L X 0.9 0.00008 -0.00002 1.1 1.2 0.9 1.0 1.1 -0.00002 0.00006 -0.00004 -0.00004 0.00004 -0.00006 -0.00006 0.00002 -0.00008 -0.00008 -0.00010 X -0.00010 O 0.9 1.0 1.1 1.2 10-0.00012 10-0.00012