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