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

1 Answer
Cesareo R.
May 17, 2016

for x< -17/68x<−1768 convexity and x > -17/68x>−1768 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+68d2dx2f(x)=72x+68, If d^2/(dx^2)f(x) < 0d2dx2f(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) > 0d2dx2f(x)>0 is concave. Solving for d^2/(dx^2)f(x) = 0d2dx2f(x)=0 we get x =-17/68 x=−1768 so for x<-17/68x<−1768 we have convexity and for x>-17/68x≻1768 concavity.

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