42. f(x) 1 -; a = 2 Зх — 1'

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
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Can you solve number 42? I want the middle steps.

a. For the following functions and values of a, find f'(a).
b. Determine an equation of the line tangent to the graph of f at the
point (a, f(a)) for the given value of a.
33. f(x)
8x; a = -3
34. f(x) = x²; a = 3
35. f(x) = 4x² + 2x; a = -2 36. f(x) = 2x³; a = 10
%3D
%3D
1
37. f(x)
; a
4
1
38. f(x)
a = 1
Vx
39. f(x)
V2r + 1; a = 4
40. f(x) = V3x; a = 12
%3D
41. f(x)
1
-;a = 5
42. f(x)
1
; а %3D 2
x + 5
Зх — 1
Transcribed Image Text:a. For the following functions and values of a, find f'(a). b. Determine an equation of the line tangent to the graph of f at the point (a, f(a)) for the given value of a. 33. f(x) 8x; a = -3 34. f(x) = x²; a = 3 35. f(x) = 4x² + 2x; a = -2 36. f(x) = 2x³; a = 10 %3D %3D 1 37. f(x) ; a 4 1 38. f(x) a = 1 Vx 39. f(x) V2r + 1; a = 4 40. f(x) = V3x; a = 12 %3D 41. f(x) 1 -;a = 5 42. f(x) 1 ; а %3D 2 x + 5 Зх — 1
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