Determine the maximum and minimum values of the functions f (x) = x² + 16/x²
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This function has a closed interval of (-4, 0), (4, 0), while passing through the origin.
I'm struggling to find the maxima and minima of the function, since this finction doesn't have a standalone constant. According to my book, f has a relative minimum if f'(x) changes from negative to positive at (c, f(c)), and a relative maximum from positive to negative at (c, f(c)).
I calculated the first derivative as 16−x2−−−−−−√−x216−x2√ and the critical points are at x=−4,0,4. I've been taught that to find the relative max/min by plugging in the critical number(s) into f(x), but in this case, zero is the only output.
One other difficulty I have is these calculations require a number from a given interval. Other than picking a number at random or testing each possiblilty, how do you find the min/max when there is no constant number in the function?
I'm struggling to find the maxima and minima of the function, since this finction doesn't have a standalone constant. According to my book, f has a relative minimum if f'(x) changes from negative to positive at (c, f(c)), and a relative maximum from positive to negative at (c, f(c)).
I calculated the first derivative as 16−x2−−−−−−√−x216−x2√ and the critical points are at x=−4,0,4. I've been taught that to find the relative max/min by plugging in the critical number(s) into f(x), but in this case, zero is the only output.
One other difficulty I have is these calculations require a number from a given interval. Other than picking a number at random or testing each possiblilty, how do you find the min/max when there is no constant number in the function?
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