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Finding the derivative and finding the equation of the tangent line Finding f'(x) from the Definition of Derivative The four steps used to find the derivative f'(x) for a function y = f(x) are summarized here. 1. Find and simplify f(x + h). 2. Find and simplify f(x + h) − f(x). 3. Find and simplify the quotient Part-b f(x +h)-f(x) h 4. Find the limit as h approaches 0; f'(x) = lim Part-a. f(x) = 2x² Find the f'(x) using the definition f'(x) = Limo f(x+h)-f(x) h After find in the f (x) in Part-a f(x +h)-f(x) h a. find f'(2) b. find f(2) c. Find the equation of the tangent line at x= 2 if this limit exists. (Use the steps given above and the lesson posted)

Finding the derivative and finding the equation of the tangent line Finding f'(x) from the Definition of Derivative The four steps used to find the derivative f'(x) for a function y = f(x) are summarized here. 1. Find and simplify f(x + h). 2. Find and simplify f(x + h) − f(x). 3. Find and simplify the quotient Part-b f(x +h)-f(x) h 4. Find the limit as h approaches 0; f'(x) = lim Part-a. f(x) = 2x² Find the f'(x) using the definition f'(x) = Limo f(x+h)-f(x) h After find in the f (x) in Part-a f(x +h)-f(x) h a. find f'(2) b. find f(2) c. Find the equation of the tangent line at x= 2 if this limit exists. (Use the steps given above and the lesson posted)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 35E
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Finding the derivative and finding the equation of the tangent line Finding f'(x) from the Definition of Derivative The four steps used to find the derivative f'(x) for a function y = f(x) are summarized here. Part -a. Part-b 1. Find and simplify f(x + h). 2. Find and simplify ƒ(x + h) — f(x). 3. Find and simplify the quotient ƒ(x + h) − f(x) h 4. Find the limit as h approaches 0; f'(x) = lim f(x)=2x² Find the f'(x) using the definition f'(x) = Lim₁ 0 f(x+h)-f(x) h f(x + h) − f(x) After find in the f'(x) in Part-a a. find f'(2) b. find f(2) c. Find the equation of the tangent line at x=2 if this limit exists. 1 (Use the steps given above and the lesson posted)
Transcribed Image Text:Finding the derivative and finding the equation of the tangent line Finding f'(x) from the Definition of Derivative The four steps used to find the derivative f'(x) for a function y = f(x) are summarized here. Part -a. Part-b 1. Find and simplify f(x + h). 2. Find and simplify ƒ(x + h) — f(x). 3. Find and simplify the quotient ƒ(x + h) − f(x) h 4. Find the limit as h approaches 0; f'(x) = lim f(x)=2x² Find the f'(x) using the definition f'(x) = Lim₁ 0 f(x+h)-f(x) h f(x + h) − f(x) After find in the f'(x) in Part-a a. find f'(2) b. find f(2) c. Find the equation of the tangent line at x=2 if this limit exists. 1 (Use the steps given above and the lesson posted)
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