Maximums and minimums

  • Thread starter ryan.1015
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In summary, the question is asking for the maximum possible value of g(1) given that g is a continuous function with a defined second derivative on the interval (-2,2), g(-2)=1, and g''>4 for all x in (-2,2). The suggested function g(x)=1-4n+(x+6)n for n greater or equal to 3 satisfies these conditions, and the OP is prompted to determine its value at x=1.
  • #1
ryan.1015
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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

 
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  • #2
You must show your work, before we can help you. Any ideas?
 
  • #3
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
 
  • #4
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
 
  • #5
Same thing but I would have said "nn is NOT an "exponential" function."
 
  • #6
What about g(x)=1-4n+(x+6)n for n greater or equal to 3?
 
  • #7
HallsofIvy said:
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.
 
  • #8
Mark44 said:
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.
 

What are maximums and minimums?

Maximums and minimums are the highest and lowest values that a function can reach within a specific interval. They are important in mathematical analysis as they provide information about the behavior of a function and can be used to optimize a system or solve problems.

How do you find maximums and minimums of a function?

To find maximums and minimums of a function, you can use a variety of methods such as graphing, differentiation, or critical points. Graphing involves plotting the function on a coordinate plane and identifying the highest and lowest points. Differentiation involves finding the derivative of the function and setting it equal to zero to solve for the critical points. The critical points are then evaluated to determine if they are maximums or minimums.

What is a critical point?

A critical point is a point on the graph of a function where the derivative is equal to zero or undefined. It can represent a maximum, minimum, or point of inflection of the function. Finding the critical points is an important step in determining the maximums and minimums of a function.

Can a function have multiple maximums or minimums?

Yes, a function can have multiple maximums or minimums. This can occur when the function has multiple critical points or when the function is periodic. In some cases, there may also be a local maximum or minimum within a larger interval that contains a global maximum or minimum.

Why are maximums and minimums important in science?

Maximums and minimums have many applications in science. They can be used to optimize systems, such as finding the ideal conditions for a chemical reaction or the most efficient design for an engineering project. They are also used in physics to determine the maximum velocity or minimum energy of a system. In biology, maximums and minimums can represent the optimal conditions for growth and survival of a species.

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