Question

The absolute maximum value of function f(x) = x³ − 3x + 2 in [0, 2] is ______.

पर्याय

• 0

• 2

• 4

• 5

Answer 1

The absolute maximum value of function f(x) = x³ − 3x + 2 in [0, 2] is 4.

Explanation

f(x) = x³ − 3x + 2 in [0, 2]

f'(x) = 3x² − 3

f'(x) = 0

3x² − 3 = 0

x²  = 1

x = ± 1

x = −1 ∉ [0, 2]

∴ x = 0, 1, 2

f(0) = 0 − 0 + 2

= 2

f(1) = (1)³ − 3 × 1 + 2

= 1 − 3 + 2

= 0

f(2) = 2³ − 3 × 2 + 2

= 8 − 6 + 2

= 4

Absolute maximum value of f(x) = 4