The maximum and minimum values of a function are found where the first derivatives are equal to zero.
First, find the first derivative of f(x) = 1 - x^4
---> f'(x) = -4x^3
Then, set f'(x) = 0
---> -4x^3 = 0 ---> x = 0
This says that any maximum or minimum occurs at the point (0,y)
At x = 0 ---> f(0) = 1 - 0^4 ---> f(0) = 1
Thus, the maximum or minimum occurs at (0, 1).
To see if it is a max or a min:
Test to the left of the point (0, 1): f'(-1) = -4(-1)^3 = 4 (since positive, the slope indicates that the graph is rising to the left of the point.
Test to the right of the point (0, 1): f'(1) = -4(1)^3 = -4 (since negative, the slope indicates that the graph is falling to the right of the point.
Thus, the point (0, 1) is a maximum.
