Local,Global Maximum and minimum

[Shiroe05]

Hi
i have a problem with this problem,lol

< link to objectionable page removed >

The problem is the number 3, part 2.

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3. Consider the function \(\displaystyle \, y\, =\, 8^x\,-\, 9\, \cdot\, 4^x\, +\, 15\, \cdot\, 2^x\, \) of x.

(1) Let X denote 2^x. Express y in terms of X.

(2) Calculate the local maximum and minimum values of y, and the values of X in (1) at which y attains them.

(3) Calculate the global maximum and minimum values of y in the interval 0 < x < log₂(7), and the values of x at which y attains them.

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i dont know how to find the local maximum and minimum, if someone can tell me a good website where i can learn about it or some tip to solve the problem
Thanks

 

[ksdhart2]

The problem is the number 3, part 2.

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3. Consider the function \(\displaystyle \, y\, =\, 8^x\,-\, 9\, \cdot\, 4^x\, +\, 15\, \cdot\, 2^x\, \) of x.

(1) Let X denote 2^x. Express y in terms of X.

(2) Calculate the local maximum and minimum values of y, and the values of X in (1) at which y attains them.

(3) Calculate the global maximum and minimum values of y in the interval 0 < x < log₂(7), and the values of x at which y attains them.

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i dont know how to find the local maximum and minimum, if someone can tell me a good website where i can learn about it or some tip to solve the problem

Well, the standard method for finding minima and maxima is to use derivatives, but given that you've posted this under "Intermediate/Advanced Algebra," I'm going to assume that you're not meant to solve it in this manner. Instead, what methods have you learned in your class to solve such problems? Are you perhaps expected to graph the function and approximate the results by "eyeballing" it? Perhaps make a table of values? Something else? The more specific and complete you can be, the better we'll be able to assist you. Thank you.