Is #f(x)=sqrt(ln(x)^2)# increasing or decreasing at #x=1#?
x = 1 meets the two branches of log graphs representng this equation, at the common point (1. 0). This is a node for the graph. f(x) is increasing for one branch and decreasing for the other.
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.So, the given equation is the combined equation for the pair
y = f(x) = + ln x and y =
For x > 1, the graph for the first is above the x-axis It is below the x-axis, for 0 < x < 1,
For the graph of the second equation in the pair, it is vice versa.
y-axis ( x = 0 ) is the asymptote.
Separately, f'(x) =
Anyway, at x = 1, y = 0 and f'(1) = +1 > 0 for one branch, and
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