Find an equation of the line tangent to the graph of 4/x^4 at (3,4/81)

题目

Find an equation of the line tangent to the graph of 4/x^4 at (3,4/81)
and 3/x^4 at (5,3/625)

答案

在点(3,4/81)求y=4/x^4 对x的偏导d(4x^(-4))/dx=-16x^(-5)把x=3代入,球的直线斜率为-16/243所以equation:y-4/81=-16/243(x-3)同理d(3x^(-4))/dx=-12x^(-5)equation:y-3/625=-12/(5^5) (x-5)