1. Let’s find the first derivative of the given function:
y ‘= (x ^ 2)’ = 2x.
2. Let us equate this derivative to zero and find the critical points:
2x = 0;
x = 0: 2;
x = 0.
Point x = 0 does not belong to the specified segment.
3. Find the value of the function at the ends of the given segment [-2; -one]:
y (-2) = (-2) ^ 2 = 4;
y (-1) = (-1) ^ 2 = 1.
The largest value of the function is at the point x = -2 and is equal to 4, the smallest value of the function is at the point x = -1 and is equal to 1.
Answer: the highest function value is 4, the lowest function value is 1.
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