Find the largest and smallest values of the function y = x ^ 8 on the segment (-1; 2)?

1. Let us find the first derivative of the function y = x ^ 8:

y ‘= 8x ^ 7.

2. Let us equate this derivative to zero:

8x ^ 7 = 0;

x ^ 7 = 0;

x = 0.

3. Find the value of the function at this point and at the ends of the specified segment [-1; 2]:

y (0) = 0;

y (-1) = 1;

y (2) = 2 ^ 8 = 256.

Then the function has the greatest value at the point x = 2, and the smallest at the point x = 0, which belongs to a given segment.

Answer: fmin = 0, fmax = 256.