Find the minimum value of the function f (x) = 2x3-3x2 (- 1 ≤ x ≤ 2), You'd better be able to draw

Find the minimum value of the function f (x) = 2x3-3x2 (- 1 ≤ x ≤ 2), You'd better be able to draw

f(x)=2x³-3x²=x²(2x-3)
∵ x²≥0
When 2x-3 is the minimum, f (x) is the minimum
∵ f (x) = 2x-3 is an increasing function in [- 1,2]
When x = - 1, the function f (x) = 2x & # 179; - 3x & # 178; gets the minimum value, f (x) min = - 5

Given that the minimum value of function f (x) = - 2x3-3x2 + 12x + 1 on [M, 1] is - 17, then M=

Finding derivative f '= - 6x ^ 2-6x + 12 = - 6 (x + 2) (x-1)
Monotone decreasing function from - infinity to - 2
Monotonically increasing from - 2 to 1
Monotonically decreasing from 1 to positive infinity
When m > - 2, the minimum value is f (m) = - 17 (x ^ 2-6) (2x + 3) = 0, so m = - 3 / 2
When m

The minimum value of function f (x) = 3x4 ^ X - 2 ^ x when x belongs to [0, positive infinity]?

Let 2 ^ x = t belong to [1, positive infinity]
Function = 3 * T ^ 2-T = 3 * (t-1 / 6) ^ 2-1 / 12
The function increases monotonically on [1, positive infinity], so when t = 1, the function is minimum
2