y=(x-1)乘三次根号下x的平方,令Y的导数等于0,那么如何求X的值?
问题描述：
y=(x-1)乘三次根号下x的平方,令Y的导数等于0,那么如何求X的值?
答
y = (x - 1) • x^(2/3)
y' = x^(2/3) + (x - 1) • (2/3)x^(-1/3)
= (5x - 2)/[3x^(1/3)]
令y' = 0
则(5x - 2)/[3x^(1/3)] = 0
=> 5x - 2 = 0
=> x = 2/5，(2/5,f(2/5))是驻点
答
y = (x-1)乘三次根号下x² = (x-1) * x^(2/3)y' = (x-1) * [x^(2/3)]' + (x-1)' * x^(2/3)= (x-1) * 2/3* x^(-1/3) + 1 * x^(2/3)= 2/3 (x-1) * x^(-1/3) + x^(2/3)= 2/3 (x-1) / x^(1/3) + x^(2/3)= [2/3 (x-1)...