Question

Consider the function f(x) = 2x³ – 3x² in the domain [-1, 2]. The global minimum of f(x) is _______

Answer 1

f(x) = 2x³ – 3x² [-1, 2]

Global Minimum t f(x) = ?

f (-1) = 2(-1)³ – 3(-1)² = -2 – 3 ⇒ f (-1) = -5

f (2) = 2(2)³ – 3(2)² = 16 – 12 ⇒ f (2) = 4

f’(x) = 6x² – 6x

f’(x) = 0 ⇒ 6x² – 6x = 0 ⇒ 6x (x - 1) = 0 ⇒ x = 0, 1

So, f (0) = 0

f (1) = 2(1)³ – 3(1)² ⇒ f (1) = -1

⇒ Key concept: In this question since it is asked for global minimum no. you have to check for all the value which are in the range of [-1, 2].

∴ Global Minimum of f(x) ⇒ f (-1) = -5