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45-48. Slopes of tangent lines Given the function f, find the slope of the line tangent to the graph of f-l at the specified point on the graph of f. 45. f(x) = Vx; (2, 4) 46. f(x) = x'; (8,2)

45-48. Slopes of tangent lines Given the function f, find the slope of the line tangent to the graph of f-l at the specified point on the graph of f. 45. f(x) = Vx; (2, 4) 46. f(x) = x'; (8,2)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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y = x ith y = f(x) + 1 -1 20 44. Derivatives of inverse functions at a point Find the derivative of the inverse of the following functions at the specified point on the graph of the inverse function. You do not need to find f-1. 39. f(x) = 3x t 4; (16, 4) (x) Sa 40. f(x) = x + 8; (10, 4)ed in s delined as2 41. f(x) = -5x + 4; (+1, 1) dt. 42. f(x) = x² + 1, forx 0; (5, 2) 0<xal 43. f(x) = tan x; (1, 7/4) TT 44. f(x) = x?t+12x 3, forx s 1; (12,-3) e toral legari 45-48. Slopes of tangent lines Given the function f, find the slope of Logari he et the line tangent to the graph of f¯ at the specified point on the graph he of f-l. 45. f(x) = Vx; (2, 4) 46. f(x) = x³; (8, 2) 47. f(x) = (x + 2)²; (36, 4) 48. f(x) = -x² + 8; (7, 1) %3D 49-52. Derivatives and inverse functions 49. Find (f)'(3) if f(x) = x' + x + 1. 50. Find the slope of the curve y f-(x) at (4,7) if the slope of the curve y = f(x) at (7, 4) is.
Transcribed Image Text:y = x ith y = f(x) + 1 -1 20 44. Derivatives of inverse functions at a point Find the derivative of the inverse of the following functions at the specified point on the graph of the inverse function. You do not need to find f-1. 39. f(x) = 3x t 4; (16, 4) (x) Sa 40. f(x) = x + 8; (10, 4)ed in s delined as2 41. f(x) = -5x + 4; (+1, 1) dt. 42. f(x) = x² + 1, forx 0; (5, 2) 0<xal 43. f(x) = tan x; (1, 7/4) TT 44. f(x) = x?t+12x 3, forx s 1; (12,-3) e toral legari 45-48. Slopes of tangent lines Given the function f, find the slope of Logari he et the line tangent to the graph of f¯ at the specified point on the graph he of f-l. 45. f(x) = Vx; (2, 4) 46. f(x) = x³; (8, 2) 47. f(x) = (x + 2)²; (36, 4) 48. f(x) = -x² + 8; (7, 1) %3D 49-52. Derivatives and inverse functions 49. Find (f)'(3) if f(x) = x' + x + 1. 50. Find the slope of the curve y f-(x) at (4,7) if the slope of the curve y = f(x) at (7, 4) is.
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