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1) Use the definition of the derivative to find f'(x) f(x) = (4x + 1)(3 – 7x³) Step 1: Step 2: Step 3: Step 4:

1) Use the definition of the derivative to find f'(x) f(x) = (4x + 1)(3 – 7x³) Step 1: Step 2: Step 3: Step 4:

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 44E
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Example 1: Find the derivative of f(x) 2x2 using definition of the derivative Solution: Step 1: Evaluate f at x + h. f(x + h) 2(x + h)?= 2x² + 4xh + 2h² Step 2: Subtract f (x) from f(x + h). f(x +h) – f(x) = 2x2 + 4xh + 2h2 – (2x2) = 4xh + 2h2 Step 3: Divide the difference of f (x + h) and f(x) by h. 4xh + 2h2 2h(2x + h) = 2(2x + h) %3D h h Step 4: Take the limit of the quotient as h approaches 0. f'(x)= lim 2(2x + h) = 2(2x + 0) = 4x %3D h-0 Therefore, f'(x) = 4x. Because the derivative of a function is also the slope, then it can also be viewed as a rate of change.
Transcribed Image Text:Example 1: Find the derivative of f(x) 2x2 using definition of the derivative Solution: Step 1: Evaluate f at x + h. f(x + h) 2(x + h)?= 2x² + 4xh + 2h² Step 2: Subtract f (x) from f(x + h). f(x +h) – f(x) = 2x2 + 4xh + 2h2 – (2x2) = 4xh + 2h2 Step 3: Divide the difference of f (x + h) and f(x) by h. 4xh + 2h2 2h(2x + h) = 2(2x + h) %3D h h Step 4: Take the limit of the quotient as h approaches 0. f'(x)= lim 2(2x + h) = 2(2x + 0) = 4x %3D h-0 Therefore, f'(x) = 4x. Because the derivative of a function is also the slope, then it can also be viewed as a rate of change.
1) Use the definition of the derivative to find f'(x) f(x) = (4x + 1)(3 – 7x3) Step 1: Step 2: Step 3: Step 4:
Transcribed Image Text:1) Use the definition of the derivative to find f'(x) f(x) = (4x + 1)(3 – 7x3) Step 1: Step 2: Step 3: Step 4:
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