No SIM 3:26 PM 43%) media.pearsoncmg.com Course Content-MATH 1720 Calculus II-Se

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No SIM 3:26 PM 43%) media.pearsoncmg.com Course Content-MATH 1720 Calculus II-Section 4 3 Calculus, Second Edition Calculus 2nd Edition Textbook Solutions | Chegg.com PEARSON Skip Directly to Table of Contents | Skip Directly to Main Content Change text size+- Show/Hide TOC GO Table of Contents 7 Logarithmic and Exponential Functions>7.1 Inverse Functions> Section 7.1 Exercises Calculus, Second Edition +1 Functions +2 Limits 39-44. 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 findf 39. f(x) = 3x + 4; (16.4) 40. Ax) =-x + 8; (10.4) 41. Rx) =-5x+4; (-1,1) 3 Derivatives 4 Applications of the Derivative 5 Integration 6 Applications of Integration 7 Logarithmic and Exponential 43·f(x)= tan x; (1, /4) 44.ffx)-2r 3, forx1; (12. -3) Functions at the 45-48. Slopes of tangent lines Given the function f, find the slope of the line tangent to the graph off specified point on the graph of 8 Integration Techniques Vx; 45, f(x) = 46·f(x) =x3; (8,2) 47,f(x) = (x + 2)2; (36,4) 9 Sequences and Infinite Series (2.4) +10 Power Series 11 Parametric and Polar Curves 12 Vectors and Vector-Valued Functions 49-52. Derivatives and inverse functions 13 Functions of Several Variables 49. Find (f(3), whre f(x) -3+x+1 14 Multiple Integration 50 Suppose the slope of the curve v = fr) at (7 4) is- Find the slope of the curve rat (4 7 =

Explanation / Answer

40)

point is (10,4)

=>f(10)=4

=>f-1(4)=10

f(x)=(1/2)x+8

=>f '(x)=(1/2)

=>f '(10)=(1/2)

when f has inverse, then (f(f-1(x)))=x

differentiate with respect to x

derivative rule: (f(g(x)))'=(f '(g(x)))*(g'(x))

=>(f '(f-1(x)))*(f-1(x))'=1

=>(f-1(x))'=1/(f '(f-1(x)))

=>(f-1(4))'=1/(f '(f-1(4)))

=>(f-1(4))'=1/(f '(10))

=>(f-1(4))'=1/(1/2)

=>(f-1(4))'=2

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