For \( f(x) = 2x^2 + 1 \), use the definition of the derivative \( f'(x) = \lim_{{h \to 0}} \frac{f(x+h) - f(x)}{h} \) to find \( f'(x) \). - \( f'(x) = 4x \) - \( f'(x) = 2x - 1 \) - \( f'(x) = 4x - 1 \) - \( f'(x) = 2x + 1 \)

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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For \( f(x) = 2x^2 + 1 \), use the definition of the derivative \( f'(x) = \lim_{{h \to 0}} \frac{f(x+h) - f(x)}{h} \) to find \( f'(x) \).

- \( f'(x) = 4x \)
- \( f'(x) = 2x - 1 \)
- \( f'(x) = 4x - 1 \)
- \( f'(x) = 2x + 1 \)
Transcribed Image Text:For \( f(x) = 2x^2 + 1 \), use the definition of the derivative \( f'(x) = \lim_{{h \to 0}} \frac{f(x+h) - f(x)}{h} \) to find \( f'(x) \). - \( f'(x) = 4x \) - \( f'(x) = 2x - 1 \) - \( f'(x) = 4x - 1 \) - \( f'(x) = 2x + 1 \)
Expert Solution
Step 1

f(x) is differentiable then 

h0limf(x+h)-f(x)h

Here f(x)=2x2+1

 

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