一、求下列函数的极值.
1、y=4x-x^2
令 y ' = 4 - 2x = 0 ===> x = 2, y(2) = 8 - 4 = 4 (极大值)
2、y=2x^3+1
令 y ' = 6x² = 0 ===> x = 0, y(0) = 0 + 1 = 1 (不是极值)
3、y=4x^3-3x+1
令 y ' = 12x² -3 = 0 ===> x = ±1/2, y( 1/2) = 1/2 - 3/2 + 1 = 0 (极小值)
y( -1/2) = -1/2 - 3/2 + 1 = -1 (极大值)
二、求下列函数指定区间的最值.
y = 4x³ - 3x + 2 , x∈[0,1]
令 y ' = 12x² -3 = 0 ===> x = ±1/2, y( 1/2) = 1/2 - 3/2 + 2 = 1 (最小值) -----1/2不必考虑
x = 0 , y(0) = 2 (起点)
x = 1 , y(1) = 3 (最大值)