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