Find the absolute maximum value and the absolute minimum val

Solution

We need to find the derivative of the given function first f(x)=4x-(5/x) f\'(x) = 4 - 5logx now, we know that the equating the derivative with 0 will give the critical points. f\'(x) = 4 - 5logx 0 = 4 - 5logx x = e^(4/5) Now, we evaluate the function at the critical points and the end points of the interval. We will get at x = 1 f(1) = -1 at x = 3 f(3) = 31/3 = 10.33 at x = e^(4/5) f(e^(4/5)) = 6.65 Absolute extrema are the largest and smallest the function will ever be and these four points represent the only places in the interval where the absolute extrema can occur so, at x = 3 we will get abs maxima and at x = 1 will give the abs minima\\ Hope this will help you!