# Help me find the largest and smallest y = x ^ 3 + 27x-10 segment [-2; 1]

1. Let’s find the first derivative of the function:

y ‘= (x ^ 3 + 27x – 10)’ = 3x ^ 2 + 27.

2. Let us equate this derivative to zero:

3x ^ 2 + 27 = 0;

3x ^ 2 = -27;

x ^ 2 = (-27): 3;

x ^ 2 = -9.

The equation has no real roots.

x ^ 2 = 9i;

x = ± 3і.

3. Find the value of the function at the ends of the back segment:

y (-2) = (-2) ^ 3 + 27 * (-2) – 10 = -8 – 54 – 10 = -8 – 64 = -72;

y (1) = 1 ^ 3 + 27 * 1 – 10 = 1 + 27 – 10 = 28 – 10 = 18.

This means the smallest value of the function on the given interval [-2; 1] at the point x = -2 and is equal to -72, and the largest value of the function at the point x = 1 and is equal to 18.

Answer: fmax = 18; fmin = -72.

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