The discussion revolves around a twice-differentiable function g, characterized by its first and second derivatives being positive for all real numbers. Given specific values of g at certain points, participants are exploring the implications of these conditions on the possible value of g at another point.
Some participants have provided insights into the nature of the function based on its derivatives, discussing the implications of increasing slope and upward concavity. The discussion is ongoing, with participants examining the possible values for g(6) based on the given conditions and values.
There is a noted absence of the multiple choice answers in the initial problem description, which may affect the direction of the discussion. Participants are working with the known values of g(4) and g(5) to infer potential outcomes for g(6).
g' > 0 for all x, so what does that tell you about the slope of g?MorganJ said:1. Let g be a twice-differentiable function with g'(x)>0 and g"(x)>0 for all real numbers of x, such that g(4)=12 and g(5) = 18. Of the following, which is the possible value for g(6)?
Yes to both.MorganJ said:If g'>0 and g">0 is the slope increasing and the concavity is upward?
MorganJ said:The choices are 15,18,21,24,27.