Find open intervals where function is concave up and concave down

label Calculus
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s= - 3r/r-2

Concave up?

Concave down?

Apr 29th, 2015

Use the second derivative to find out concavity

s' = (r-2)(-3) - (-3r)(1) / (r-2)^2

= 6 / (r - 2)^2

s" = (r-2)^2(0) - 6(2(r - 2) / (r - 2)^4

= -12 / (x - 2)^3

which is negative for x > 2  and positive for x < 2

so,

the function is concave up in the interval (- infinity, 2)

and concave down in the interval (2, infinity)

Apr 29th, 2015

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Apr 29th, 2015
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Apr 29th, 2015
Oct 21st, 2017
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