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# help

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For a real number x, find the minimum value of (x + 4)(x + 1)(x - 1)(x - 4).

Dec 14, 2019

#1
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(x^2-16)(x^2-1)

x^4 -16x^2 - x^2 + 16

x^4 -17x^2+16     take derivative and set = 0

4x^3-34x = 0

2x(2x^2-17)

x = 0       2x^2 = 17     x^2 = 8.5   x = +-sqrt8.5

SUb these values in to the original equation to see which produces the smalles result

you will find at x = sqrt 8.5    or   sqrt -8.5    the result will be the minimum (-56.25)

at x = 0 the function = 16

Here is a graph:

https://www.desmos.com/calculator/l4gbkfzoa7

Dec 14, 2019
edited by ElectricPavlov  Dec 14, 2019

#1
0

(x^2-16)(x^2-1)

x^4 -16x^2 - x^2 + 16

x^4 -17x^2+16     take derivative and set = 0

4x^3-34x = 0

2x(2x^2-17)

x = 0       2x^2 = 17     x^2 = 8.5   x = +-sqrt8.5

SUb these values in to the original equation to see which produces the smalles result

you will find at x = sqrt 8.5    or   sqrt -8.5    the result will be the minimum (-56.25)

at x = 0 the function = 16

Here is a graph:

https://www.desmos.com/calculator/l4gbkfzoa7

ElectricPavlov Dec 14, 2019
edited by ElectricPavlov  Dec 14, 2019