Question

Please solve equation for maximum and minimum

Answer 1

17^(1/11), which occurs at x=9

Explanation:

To find the Absolute Extrema in a set of points, you need to evaluate (plug in) the endpoints, and maxima/minima of the equations and figure out the greatest and lowest ones.
1.) By using this method, the first step is to find the Relative Maximums/Minimums of these areas. We can do this by finding the derivative of the equation, and setting that equal to 0 and solving.
`(d)/(dx) (x^2-64)x^{(1)/(11)} = (x^2-64)^(-10/11) * 2x`. If we set this equal to 0, we will find that x = 0. Therefore, x=0 is a minimum. Since this point belongs to the interval of [-8, 9], we can use it.

2.) Plug the endpoints of the interval and the result from our calculations. If we do this, we get f(-8)=0, f(9) = 17^(1/11), f(0)=0
3.) Since we are finding the Maxima, we look for the greatest value, which is 17^(1/11), which occurs at x=9