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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?
HallsofIvy said:Same thing but I would have said "nn is NOT an "exponential" function."
Pere, this one, too.What about g(x)=1-4n+(x+6)n for n greater or equal to 3?
Mark44 said:I think your reply pertains to a different question...
Pere, this one, too.
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.
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.
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.
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.
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.