Find the largest and smallest values of the function y = 6-4x-2x ^ 2 on the segment [0; 3].

Find the derivative of the function:

y ‘= -4 – 4x;

Let’s find the critical points:

-4 – 4x = 0;

-4x = 4;

x = 4 / -4;

x = -1;

Let’s calculate the value of the function at the critical point and at the ends of the segment:

y (-1) = 6 – 4 * (-1) – 2 * (-1) ^ 2 = 6 + 4 – 2 = 8;

y (0) = 6 – 4 * 0 – 2 * 0 ^ 2 = 6;

y (3) = 6 – 4 * 3 – 2 * 3 ^ 2 = 6 – 12 – 18 = -24;

ynaib = 8;

unaim = -24.