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

question 26

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?

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Definitions:

Analogue Methodology

A research method that uses analogous situations or simulations to study psychological phenomena or treatments in a controlled environment.

Ethical Obstacles

Challenges or issues in research that arise from moral concerns or considerations, often related to the treatment of research participants.

Analogue Methodology

A research approach that simulates real-world conditions in a controlled environment to study behavioral processes or psychological phenomena.

Acceptable Simplifications

The process of reducing complexity in a model or explanation while still retaining a reasonable level of accuracy.