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.
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