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Use calculus to find the maximum and minimum values of the function f(x)=e^((x^7)-x) in...
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The function `f(x)=e^((x^7)-x)`
The extreme points of the function are obtained by solving the equation f'(x) = 0
f'(x) = `e^(x^7 - x)*(7x^6 - 1)`
`e^(x^7 - x)*(7x^6 - 1) = 0`
=> `7x^6 = 1`
=> `x^6 = 1/7`
The real root of the equation greater than -1 and less than 0 is at `x = -(1/7)^(1/6)` .
The function `f(x)=e^((x^7)-x)` has a maximum at `x = -(1/7)^(1/6)` .
Posted by justaguide on April 3, 2012 at 9:01 AM (Answer #1)
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