The expression f(x+h)-f(x) h f(x) = 7x² + 2x The difference quotient is (Simplify your answer.) for h#0 is called the difference quotient. Find and simplify the difference quotient for the following function. ...
The expression f(x+h)-f(x) h f(x) = 7x² + 2x The difference quotient is (Simplify your answer.) for h#0 is called the difference quotient. Find and simplify the difference quotient for the following function. ...
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Difference Quotient Exercise**
The expression \(\frac{f(x + h) - f(x)}{h}\) for \(h \neq 0\) is called the difference quotient. Find and simplify the difference quotient for the following function.
\[ f(x) = 7x^2 + 2x \]
---
The difference quotient is [ ].
(Simplify your answer.)
---
In this exercise, students are asked to find and simplify the difference quotient for the quadratic function \(f(x) = 7x^2 + 2x\). The task involves applying the definition of the difference quotient, which is an important concept in calculus used to approximate the derivative of a function at a point.
To solve the problem, students should:
1. Substitute \(f(x + h)\) into the function.
2. Expand and simplify the expression \(\frac{f(x + h) - f(x)}{h}\).
3. Simplify the resulting expression by canceling out terms and dividing by \(h\).
Finally, students need to submit their simplified form of the difference quotient in the provided space.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F23a27a63-bc63-4fb5-b83d-deee68ee526f%2F4f7392d4-bf99-4e91-99ee-612c7f8e8d31%2F2lagifb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Difference Quotient Exercise**
The expression \(\frac{f(x + h) - f(x)}{h}\) for \(h \neq 0\) is called the difference quotient. Find and simplify the difference quotient for the following function.
\[ f(x) = 7x^2 + 2x \]
---
The difference quotient is [ ].
(Simplify your answer.)
---
In this exercise, students are asked to find and simplify the difference quotient for the quadratic function \(f(x) = 7x^2 + 2x\). The task involves applying the definition of the difference quotient, which is an important concept in calculus used to approximate the derivative of a function at a point.
To solve the problem, students should:
1. Substitute \(f(x + h)\) into the function.
2. Expand and simplify the expression \(\frac{f(x + h) - f(x)}{h}\).
3. Simplify the resulting expression by canceling out terms and dividing by \(h\).
Finally, students need to submit their simplified form of the difference quotient in the provided space.
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