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How do you determine whether the function # f(x) = 2x^3 + 3x^2 - 432x # is concave up or concave down and its intervals?

1 Answer

Sep 24, 2015

f(x) is concave down on #(-oo;-1/2)# and concave up on #(-1/2;oo)#

Explanation:

You have to investigate the sign of the second derivative around its zero points (inflection points).

In this case,

#f'(x)=6x^2+6x-432#
#f''(x)=12x+6#

#therefore f''(x)=0iffx=-1/2#

#therefore AAx<-1/2=>f''(x)<0# and hence the concavity is down.

#therefore AAx >-1/2=>f''(x)>0# and hence the concavity is up.

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