For f(x) = x² near x = 2, the local slope is 4. What linear estimate describes the change in f for an increase of 0.01 in x?
Answer & explanation
Approximately 0.04.
The tangent estimate uses slope times input change. The exact calculation includes the squared increment as well. Its small extra term shows why a close approximation is still an approximation.
How Not to Be Wrong
Chapter 2 · Straight Locally, Curved Globally
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