Let $f ( x ) = x ^ { 3 } - 4 x ^ { 2 }$

Essay

Let $f ( x ) = x ^ { 3 } - 4 x ^ { 2 }$ (a) Find a linear approximation of f at x = 1.(b) Use this linear approximation to predict the value of the function at -1, 0, 0.9, 1.1, 2, and 3.(c) Make a table comparing your estimates with the actual function values. Discuss what this tells you about the linear approximation.(d) Graph the original function and its linear approximation over the interval [-1; 3]. What does the graph tell you about the size of the difference between the function values and the linear approximation values?