# For what values of x is #f(x)= -5x^3+x^2+4x-12 # concave or convex?

##### 1 Answer

#### Explanation:

#f(x)# is convex when#f''(x)>0# .

#f(x)# is concave when#f''(x)<0# .

Find

#f(x)=-5x^3+x^2+4x-12#

#f'(x)=-15x^2+2x+4#

#f''(x)=-30x+2#

The concavity could change when

#f''(x)=0#

#-30x+2=0#

#x=1/15#

Analyze the sign surrounding the point

When

When

When

Thus,

Graph of

graph{-5x^3+x^2+4x-12 [-22.47, 28.85, -20.56, 5.1]}

The concavity does seem to shift very close to