For what values of x is #f(x)=(3x-2)(4x+2) (x+3)# concave or convex?

1 Answer
Cesareo R.
May 17, 2016

for #x< -17/68# convexity and #x > -17/68# concavity

Explanation:

For a twice continuous function like the one proposed, the concavity or convexity is determined by the second derivative sign.
#d^2/(dx^2)f(x)=72x+68#, If #d^2/(dx^2)f(x) < 0# the curvature is considered as convex because the area region contained below is a convex set. If #d^2/(dx^2)f(x) > 0# is concave. Solving for #d^2/(dx^2)f(x) = 0# we get #x =-17/68 # so for #x<-17/68# we have convexity and for #x>-17/68# concavity.

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