How Large Can g(1) Be Given g'' > 4 on (-2,2)?

[ryan.1015]

Homework Statement

suppose that g is a function defined and continuous on (-2,2) and that g" exists on the open interval (-2,2). if g(-2)=1 and g">4 for all x in (-2,2), how large can g(1) possibly be?

Homework Equations

The Attempt at a Solution

 

[Pere Callahan]

You must show your work, before we can help you. Any ideas?

 

[ryan.1015]

i have no idea. we haven't done these type of problems before. usually he just gives us an equation and just asks us to find the max

 

[ryan.1015]

i have no idea. we haven't done any problems like this before. Usually he just gives us an equation and asks for the max

 

[HallsofIvy]

Same thing but I would have said "nⁿ is NOT an "exponential" function."

 

[Pere Callahan]

What about g(x)=1-4ⁿ+(x+6)ⁿ for n greater or equal to 3?

 

[Mark44]

Same thing but I would have said "nⁿ is NOT an "exponential" function."

I think your reply pertains to a different question...

What about g(x)=1-4n+(x+6)n for n greater or equal to 3?

Pere, this one, too.

 

[Pere Callahan]

I think your reply pertains to a different question...


Pere, this one, too.

I think my post belongs to this question. The function g I suggested satisfies g(-2)=1 and g''>4 in (-2,2). I intended to motivate the OP to check what g(1) is and how this relates to his question.