• Support PF! Buy your school textbooks, materials and every day products Here!

Twice-differentiable Function and Etc.

  • Thread starter MorganJ
  • Start date
  • #1
32
0
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 :-(
 

Answers and Replies

  • #2
33,167
4,852
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.
 
  • #3
32
0
If g'>0 and g">0 is the slope increasing and the concavity is upward? The choices are 15,18,21,24,27.
 
  • #4
33,167
4,852
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.
 

Related Threads for: Twice-differentiable Function and Etc.

  • Last Post
Replies
2
Views
3K
Replies
2
Views
10K
Replies
3
Views
1K
Replies
3
Views
4K
  • Last Post
Replies
5
Views
1K
Replies
10
Views
3K
Replies
18
Views
2K
  • Last Post
Replies
2
Views
2K
Top