In part A, I understand the funciton to by y = 2(sqrt x) -3x. Is that correct? the interval is [1,4]. In this case you can make a table of the value of the function when x is 1, 2, 3, 4. In that range it is always decreasing, so the maximum would be at x=1 and the minimum at x=4. If you know derivatives, then the derivative of the function y is 1/(sqrt(x)) - 3. In the interval [1,4] this derivative is always negative, so the function is decreasing on the interval and the maximum is at x=1 and the minimum is at x=4.
In part B, I understand the function to be cuberoot(x+1) + cuberoot(1-x). Is this correct? The interval is [-1,1]. If you compute the function at -1, 0, and 1 it has a smaller value at -1 than it does at 0 and a smaller values at 1 than it does at 0. And if we plot the function at x=.1 and x=-.1 we find that it's less than the