How many points of inflection does the function #f(x) = (pi/3)^((x^3)-8)# have?
2 Answers
One.
To find the points of inflection of any function, we compute the function's derivative then find the points where the derivative equals zero. In this case, we use the chain rule: let
There is no need to simplify this function any further. We know that for
Clearly,
Two points of inflections:
Explanation:
A point of inflection can be obtained when
Using the chain rule: let
Since:
only possible solution is when:
Hence two points of inflections:
Note that when