证明曲线x^2/3+y^2/3=a^2/3(注a>0常数,2/3为次方)上任意点处的切线介于两坐标轴之间的线段长为定长
问题描述：
证明曲线x^2/3+y^2/3=a^2/3(注a>0常数,2/3为次方)上任意点处的切线介于两坐标轴之间的线段长为定长
答
记a^(2/3)=A,原式可化为:y=[A-x^(2/3)]^(3/2)=f(x)对x求导:y=[A-x^(2/3)]^(1/2)*[-x^(-1/3)]=-[f(x)]^(1/3)*x^(-1/3)故(m,n)处切线为:y=-n^(1/3)*m^(-1/3)(x-m)+n令x=0,y=n^(1/3)*A令y=0,x=m^(1/3)*A介于坐标轴间的...