Graph the cube root function and analyze the minimum and maximum on the given interval. f(x)=4x√3; [1,8] a)maximum: 8, minimum: 0 b) maximum: 8, minimum: 4 c) 1/2, minimum: 0 d); 1/2, minimum: 14

The cube root function begins in Quadrant III and ends in Quadrant I.  It passes through the origin, (0,0).

Did you mean 4*∛3?  or 4*x*√3?    I will assume you meant the former, not the latter.

The graph of 4*∛3 looks the same as that of ∛3 except that the whole graph has been stretched vertically by a factor of 4.

This function has neither maximum nor minimum.

I urge you to go back to the original problem and ensure that you have copied it exactly as it was given.