Find the absolute minimum value on (0,infinity) for f(x)=(x+8)(x-4)^2

1 answer:

7 0

It is a continuous function whose derivative exists. Therefore, extreme values are either on the edge of the interval [0 , infinity], or at the zero slope points where the derivative is zero. So calculate the value of the function at x = 0; then look at the value of the function when x increases to infinity (larger and larger values). Looks like the larger x is, the larger the function, so it tends to + infinity as well. Thankfully, we are looking for an absolute minimum, therefore the infinity value is out. Then calculate the derivative, and find the x values for which it is zero. Then calculate the value of the function for those zero slope x values, and compare to the value of the function at the edge, x = 0. Finally, pick the x value for which the function value is lowest. That is your absolute minimum value.

Hope this helps!! (If not I'm sorry!)

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