Use the limit definition to find the derivative of the function. f(x) = x² + 5x – 5 - f(x + h) – f(x) First, find h |(2x+h+5)/h Preview Next, simplify the numerator. h(2x+h+5) Preview Divide out the h. 2x+h+5 Preview So now, find the limit f(x + h) – f(x) lim = 2x+5 Preview h→0 h

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Use the limit definition to find the derivative of the function.
f(x) = x² + 5x – 5
f(x + h) – f(x)
-
First, find
h
(2x+h+5)/h
Preview
Next, simplify the numerator.
h(2x+h+5)
Preview
Divide out the h.
2x+h+5
Preview
So now, find the limit
f(x + h) – f(x)
lim
= 2x+5
Preview
h→0
h
Transcribed Image Text:Use the limit definition to find the derivative of the function. f(x) = x² + 5x – 5 f(x + h) – f(x) - First, find h (2x+h+5)/h Preview Next, simplify the numerator. h(2x+h+5) Preview Divide out the h. 2x+h+5 Preview So now, find the limit f(x + h) – f(x) lim = 2x+5 Preview h→0 h
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