Question

What is the equation of the tangent line of `f(x)=2x-x^2` at `x=0`?

Answer 1

`y=2x`

Explanation:

`"the slope of the tangent line is the derivative of "f(x)`
`"at x = 0"`

`rArrf'(x)=2-2xrArrf'(0)=2=m_("tangent")`

`"and "f(0)=0rArr(0,0)`

`rArry=2xlarrcolor(red)"equation of tangent"`
graph{(y-2x+x^2)(y-2x)=0 [-10, 10, -5, 5]}