Use the definition of the derviative to compute the derivative of f(x)= 1-7x2 at the specific point x=2 Evaluate the limit by using algebra to simplify the difference quotient (in first answer ) and then evaluating the limit (in the second answer ).   f'(2)=lim→0 (f(2+h)-f(2)) / (h) Part 2: The derivative function   Use the definition of the derivative to compute the derivative of the function f(x)1-7x2 at an arbitrary point x=2  Evaluate the limit by using algebra to simplify the difference quotient (in first answer ) and then evaluating the limit (in the second answer).   f'(x)= h→0  (f(x+h)-f(x)) / (h)   Part 3: The tangent line   Now let’s calculate the tangent line to the function f(x)= 1-7x2 at x=5   By using f′(x) from part 2, the slope of the tangent line to f at x=5  is f'(5)=   The tangent line to f at x=5 passes through the point (5,f(5)) on the graph of f. (Enter a point in the form (2,3) including the parentheses.)   An equation for the tangent line to f  at x=5 is y=

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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Use the definition of the derviative to compute the derivative of f(x)= 1-7x2 at the specific point x=2 Evaluate the limit by using algebra to simplify the difference quotient (in first answer ) and then evaluating the limit (in the second answer ).
 
f'(2)=lim→0 (f(2+h)-f(2)) / (h)



Part 2: The derivative function

 

Use the definition of the derivative to compute the derivative of the function f(x)1-7x2 at an arbitrary point x=2  Evaluate the limit by using algebra to simplify the difference quotient (in first answer ) and then evaluating the limit (in the second answer).
 
f'(x)= h→0  (f(x+h)-f(x)) / (h)

 

Part 3: The tangent line

 

Now let’s calculate the tangent line to the function f(x)= 1-7x2 at x=5
 
    1. By using f′(x) from part 2, the slope of the tangent line to f at x=5  is f'(5)=
 
    1. The tangent line to f at x=5 passes through the point (5,f(5)) on the graph of f. (Enter a point in the form (2,3) including the parentheses.)
 
  1. An equation for the tangent line to f  at x=5 is y=
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