For the function f(x) 3x²z+9, evaluate and fully simplify each of the following. f(a+h)- f(a+h)-f(x) h
For the function f(x) 3x²z+9, evaluate and fully simplify each of the following. f(a+h)- f(a+h)-f(x) h
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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![**Problem Statement for Educational Website**
For the function \( f(x) = 3x^2 - x + 9 \), evaluate and fully simplify each of the following expressions:
1. \( f(x + h) = \) [______]
2. \( \frac{f(x + h) - f(x)}{h} = \) [______]
*Instructions:*
- To start, substitute \( x + h \) directly into the function \( f(x) \) to find \( f(x + h) \).
- Then, use the result of \( f(x + h) \) in the second expression and perform algebraic simplifications step by step to simplify the difference quotient \( \frac{f(x + h) - f(x)}{h} \).
This exercise is designed to help understand the application of functions and the process of finding the derivative through the limit definition.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f7f7e91-311f-40b2-8ef2-058480eb16a0%2F6108e3ff-fb2f-4e18-b68b-13952d27dcea%2Fw27vi4a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement for Educational Website**
For the function \( f(x) = 3x^2 - x + 9 \), evaluate and fully simplify each of the following expressions:
1. \( f(x + h) = \) [______]
2. \( \frac{f(x + h) - f(x)}{h} = \) [______]
*Instructions:*
- To start, substitute \( x + h \) directly into the function \( f(x) \) to find \( f(x + h) \).
- Then, use the result of \( f(x + h) \) in the second expression and perform algebraic simplifications step by step to simplify the difference quotient \( \frac{f(x + h) - f(x)}{h} \).
This exercise is designed to help understand the application of functions and the process of finding the derivative through the limit definition.
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