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Which is use to compute the derivative of a function? * f(x+h)-f(x) lim h-0 h Option 1 O f'(x)=0 P'(x)=nX n-1 Option 3 All of these

Which is use to compute the derivative of a function? * f(x+h)-f(x) lim h-0 h Option 1 O f'(x)=0 P'(x)=nX n-1 Option 3 All of these

Calculus: Early Transcendentals
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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**Understanding Derivatives: Key Concepts in Calculus** **Question:** Which is used to compute the derivative of a function? * 1. **Option 1:** - Formula: \[ \lim_{{h \to 0}} \frac{{f(x+h) - f(x)}}{h} \] - **Explanation:** This represents the definition of the derivative, illustrating the limit process to determine the slope of the tangent line at any point on the function. 2. **f'(x) = 0** - **Explanation:** This equation implies that the derivative of the function is zero, indicating a horizontal tangent line or a potential local maximum or minimum. 3. **Option 3:** - Formula: \[ f'(x) = nX^{n-1} \] - **Explanation:** This denotes the power rule in differentiation, used to find the derivative of functions of the form \(x^n\). 4. **All of these** - **Explanation:** This option considers whether all previous options are applicable in computing derivatives under different contexts or interpretations. **Choose the correct option that directly applies to differentiating a function.**
Transcribed Image Text:**Understanding Derivatives: Key Concepts in Calculus** **Question:** Which is used to compute the derivative of a function? * 1. **Option 1:** - Formula: \[ \lim_{{h \to 0}} \frac{{f(x+h) - f(x)}}{h} \] - **Explanation:** This represents the definition of the derivative, illustrating the limit process to determine the slope of the tangent line at any point on the function. 2. **f'(x) = 0** - **Explanation:** This equation implies that the derivative of the function is zero, indicating a horizontal tangent line or a potential local maximum or minimum. 3. **Option 3:** - Formula: \[ f'(x) = nX^{n-1} \] - **Explanation:** This denotes the power rule in differentiation, used to find the derivative of functions of the form \(x^n\). 4. **All of these** - **Explanation:** This option considers whether all previous options are applicable in computing derivatives under different contexts or interpretations. **Choose the correct option that directly applies to differentiating a function.**
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