Question

What is the equation of the tangent line of `f(x)=cos^3x/x^2` at `x=pi/3`?

Answer 1

`y=-27(sqrt(3)pi+2)/(8*pi^3)*x+(9*cos(pi/3)^3)/pi^2+9*(sqrt(3)pi+2)/(8*pi^2)`

Explanation:

We get
`f(pi/3)=(9cos(pi/3)^3)/pi^2`
`f'(x)=-cos(x)^2(3sin(x)*x+2cos(x))/x^3`

`f'(pi/3)=-27*(sqrt(3)pi+2)/(8*pi^3)`
This is the slope of the tangent line and the point
`P(pi/3;(9cos(pi/3)^3)/pi^2)`