The degree of the polynomial is 2. This is because the highest exponent in the polynomial is 2.
The leading coefficient is 2. This is because it is the coefficient of the term with the highest degree, which is x^(2/3).
To find the critical points, set the derivative of the function equal to 0 and solve for x. In this case, the derivative is f'(x) = 4x^(1/3) - 2x^(-1/3). Solving for x, we get x = 1/2. Therefore, the critical point of the function is (1/2, 0).
The domain of the function is all real numbers except for x = 0. This is because the function is undefined at x = 0 due to the presence of x^(-1/3).
To find the x-intercepts, set the function equal to 0 and solve for x. In this case, we get x = 0 and x = 3/4. Therefore, the x-intercepts of the function are (0,0) and (3/4,0). To find the y-intercept, plug in x = 0 into the function and we get y = 0. Therefore, the y-intercept of the function is (0,0).