作业题:它是极大值还是极小值
f'(x) = acosx + cos(3x);
极值点 f'(π/3) = 0,即 f'(π/3) = acos(π/3) + cos(π) = 0,
a/2 -1 = 0,a = 2;
f''(x) = -2sinx - 3sin(3x);
f''(π/3) = -2sin(π/3) - 3sin(π) < 0,极值是极大值 。
极大值 f(π/3) = 2sin(π/3) + [ sin(3π) ]/3 = 2 * √3/2 + 0 = √3 。
极值判别方法:若 f'(x0) = 0,则 x = x0 是驻点;
若f''(x0) > 0,驻点是极小点;
若f''(x0) < 0,驻点是极大点;
若f''(x0) = 0 且f'''(x0) ≠ 0,驻点是拐点 。
热门标签: