text: a. f'(x) = (4/3)x^(1/3)+(4/3)*x^(-2/3) = 0 for x = -1. This is the only point where the tangent is horizontal.\nb. from a. f'(x) = infinite for x = 0 making the tangent vertical.\nc. from a. follows the extreme max/min at x = -1. Since f''(x) = (1/3)x^(-2/3) - (2/3)x^(-5/3) = 1 > 0 for x = -1 the extreme at x = -1 is minimum.\nd. Since within the given interval the function is final and has only one minimum that is not at the end of the interval the function is concave downward (I would say upward) meaning from f(-8) = 8 monotonically decreases to the minimum f(-1) = -3 and monotonically increases again to f(8) = 24 which is then absolute maximum..\n\nn.b. you can go to excell and plot the function.