Question

What is the equation of the line tangent to `f(x)=x^2-3x` at `x=2`?

Answer 1

`y=x-4`

Explanation:

`"to obtain the equation of the tangent we require the "`
`"slope and a point on it"`

`y-b=m(x-a)`

`"slope "=f'(x)" at x = 2"`

`f'(x)=2x-3rArrf'(2)=4-3=1`

`f(2)=4-6=-2rArr(a,b)=(2,-2)`

`y+2=x-2`

`y=x-4larrcolor(red)"equation of tangent"`