# 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