Identify the function's local and absolute extreme values, if any, saying where they occur.
-$$f ( r ) = ( r - 10 ) ^ { 3 }$$
A) local minimum: x = 0
B) no local extrema
C) local minimum: x = 10
D) local minimum: x = 0; local maximum: x = 10

Question

Quizplus · Accepted Answer

The function $f(r) = (r - 10)^3$ is a cubic function with only one critical point at $r = 10$, where its derivative equals zero. However, since the function is cubic and the coefficient of the highest power term is positive, it decreases before and increases after $r = 10$ without changing concavity. Therefore, it does not have a local minimum or maximum at $r = 10$, meaning it has no local extrema.

Identify the Function's Local and Absolute Extreme Values, If Any f(r)=(r−10)3f ( r ) = ( r - 10 ) ^ { 3 }f(r)=(r−10)3

Identify the Function's Local and Absolute Extreme Values, If Any $f ( r ) = ( r - 10 ) ^ { 3 }$