Let $f ( x ) = x ^ { 2 / 3 }.$

Essay

Let $f ( x ) = x ^ { 2 / 3 }.$ (a) Find a linear approximation of f at x = 8:
(b) Use this linear approximation to estimate the value of the function at 7, 9, 7.99, and 8.01.(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 [7; 9]. What does the graph tell you about the size of the difference between the function values and the linear approximation values?