Find the absolute maximum and absolute minimum values of f on the give

1.	Find the absolute maximum and absolute minimum values of f on the given interval.f(x) = 1 – 2x – x2, [-4, 1]
Answer» f(x) = 1 – 2x – x² f'(x) = -2 – 2x f'(x) = 0 ⇒ 2x = -2 ⇒ x = -1; The points are -4, -1, 1 At x = -4, f(x) = 1 – 2(-4) – (-4) = 1 + 8 – 16 = -7 At x = -1, f(x) = 1 – 2 (-1) – (-1) = 1 + 2 – 1 = 2 At x = 1, f(x) = 1 – 2 (1) – (1) = 1 – 2 – 1 = – 2 Therefore, the absolute minimum is -7 and the absolute maximum is 2.

Find the absolute maximum and absolute minimum values of f on the given interval.f(x) = 1 – 2x – x2, [-4, 1]

Answer»

f(x) = 1 – 2x – x²

f'(x) = -2 – 2x

f'(x) = 0 ⇒ 2x = -2 ⇒ x = -1; The points are -4, -1, 1

At x = -4, f(x) = 1 – 2(-4) – (-4) = 1 + 8 – 16 = -7

At x = -1, f(x) = 1 – 2 (-1) – (-1) = 1 + 2 – 1 = 2

At x = 1, f(x) = 1 – 2 (1) – (1) = 1 – 2 – 1 = – 2

Therefore, the absolute minimum is -7 and the absolute maximum is 2.