Determine the point of inflection and discuss the concavity of the graph of ,f(x)=x^4-4x^3?

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Answer 1 · 2018-07-15T12:01:09

#x=0,y=0# and #x=2,y=-14#

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

#f''(x)=12x^2-24x#

#f'''(x)=24x-24#
solving #f''(x)=0# we get
#x(12x-24)=0#

so #x=0# or #x=2#
and

#f'''(0)=-24# there is a change from convex to concave

#f'''(2)=24# there is a change from concave to convex.
further we have

#f(2)=-14#

#f(0)=0#