Answer
Local Maximum: (-3,-27)
Local Minimum: N/A
Domain: (-∞, ∞)
Range: [-27, ∞)
See graph below
Work Step by Step
Given: $y = x^4 + 4x^3$ [-5, 5] by [-30, 30] for viewing window
On desmos, click on the wrench icon in the top right corner
Under x-axis, change the bounds of the x-axis to that stated in the problem: [-5, 5]
Under y-axis change the bounds of the y-axis to that stated in the problem: [-30, 30]
The gray dots in the graph represent the intercepts of the function and the local minimum and maximum points.
Local Maximum: (-3,-27)
Local Minimum: N/A
Domain: (-∞, ∞)
Range: [-27, ∞)