Twice-differentiable Function and Etc.

[MorganJ]

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)?



2.I honestly have no idea where to start :-(

 

[Mark44]

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)?

g' > 0 for all x, so what does that tell you about the slope of g?

g'' > 0 for all x, so what does that tell you about the concavity of g?

I take it that this is a multiple choice problem, but you didn't include the possible answers in your problem description.

 

[MorganJ]

If g'>0 and g">0 is the slope increasing and the concavity is upward? The choices are 15,18,21,24,27.

 

[Mark44]

If g'>0 and g">0 is the slope increasing and the concavity is upward?

Yes to both.

The choices are 15,18,21,24,27.

You know that g(4) = 12 and g(5) = 18. If the function happened to be a straight line, its slope would be (18 -12)/(5 -4) = 6, so in that case, g(6) would be 24.

The graph of g is not a straight line, since g'' > 0. This information eliminates all but one of the possible choices.