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(a) Find the vertical and horizontal asymptotes.(b) Find the intervals of increase or decrease.(c) Find the local maximum and minimum values.(d) Find the intervals of concavity and the inflection points.(e) Use the information from parts $(a)-(d)$ to sketch the graph of $f .$$$f(x)=\ln (1-\ln x)$$
a) V.A. $x=0, x=e, \quad$ No H. A.b) Decreasing: $0<x<e$c) No Maxima or Minimad) The function is concave up in $(0,1) .$The function is concave down in $(1, e)$Inflection point $-x=1$e) The graph has two vertical asymptotes, that is the $y$ -axis and the line $x=e$There is no Horizontal asymptote.There is no maxima/minima.The green dot is the Inflection point.
Calculus 1 / AB
Calculus 2 / BC
Applications of Differentiation
How Derivatives Affect the Shape of a Graph
Missouri State University
Harvey Mudd College
University of Michigan - Ann Arbor
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