What are the points of inflection, if any, of #f(x)= (pi/3)^((x^3-8) #?
1 Answer
Jan 8, 2017
Explanation:
Taking logarithms and differentiating,
Solving,
graph{1.4461ln y-0.04612x^3=0 [-5, 5, 0, 0, 5]}.
Further differentiation for y''' reveals that
So, the points of inflexion (POI) are
At these points, the tangent crosses the graph, to reverse its
sense of rotation, and change the form of the graph, from convexity
to concavity or vice versa.
See these effects in the inserted Socratic graph