2 Let f(x) = 3 – x²|] Estimate f'(1)d (Hint: h = 0.0001)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Transcription for Educational Website:**

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Let \( f(x) = |3 - x^2| \). Estimate \( f'(1) \) (Hint: \( h = 0.0001 \)).

**Explanation:**

This exercise asks you to estimate the derivative of a function at a specific point using a small increment, \( h \). The function given is an absolute value function, which can affect the approach to finding the derivative due to potential sharp points. The hint provides a small value for \( h \), suggesting a numerical approximation method, likely the difference quotient:

\[ f'(x) \approx \frac{f(x+h) - f(x)}{h} \]

By substituting \( x = 1 \) and \( h = 0.0001 \), you'll be able to estimate the derivative \( f'(1) \).

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This transcription can assist students in applying numerical methods to estimate derivatives, particularly when dealing with piecewise-defined functions or functions with absolute values.
Transcribed Image Text:**Transcription for Educational Website:** --- Let \( f(x) = |3 - x^2| \). Estimate \( f'(1) \) (Hint: \( h = 0.0001 \)). **Explanation:** This exercise asks you to estimate the derivative of a function at a specific point using a small increment, \( h \). The function given is an absolute value function, which can affect the approach to finding the derivative due to potential sharp points. The hint provides a small value for \( h \), suggesting a numerical approximation method, likely the difference quotient: \[ f'(x) \approx \frac{f(x+h) - f(x)}{h} \] By substituting \( x = 1 \) and \( h = 0.0001 \), you'll be able to estimate the derivative \( f'(1) \). --- This transcription can assist students in applying numerical methods to estimate derivatives, particularly when dealing with piecewise-defined functions or functions with absolute values.
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