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.
A twice-differentiable function is a mathematical function that can be differentiated twice. This means that the function has a well-defined derivative at every point in its domain, and the derivative itself is also differentiable.
A twice-differentiable function is different from a once-differentiable function in that it can be differentiated twice, while a once-differentiable function can only be differentiated once. This means that a twice-differentiable function has a smoother and more well-defined curve compared to a once-differentiable function.
A twice-differentiable function is significant in real-life applications because it represents a function that is continuous and has a well-defined slope at every point. This makes it useful in modeling various phenomena in fields such as physics, economics, and engineering.
No, a twice-differentiable function cannot have discontinuities. This is because a function must be continuous in order to be differentiable, and a twice-differentiable function must also have a continuous derivative. Discontinuities would result in undefined or infinite derivatives, which would violate the definition of a twice-differentiable function.
A function can be determined to be twice-differentiable by checking if it is continuously differentiable and if its derivative is also differentiable. This can be done by using the definition of differentiability, as well as various differentiation rules and techniques.