Question

What is the equation of the tangent line of `f(x) =x^2-x+4` at `x=2`?

Answer 1

`y=3x` is the equation of the tangent line

Explanation:

I hope I still recall how to do this haha but some other nice people will correct me if I'm wrong :)

First thing to remember is that `color (red) (f'(x)=m)` (the slope) and that the equation of a line is `color (blue) (y=mx+b)`

So, `f(x)=x^2-x+4 =>f'(x)=2x-1`

Since `f'(x)=m`, at `x=2`, we have, `m=2(2)-1=3`

From our equation, `f(x)=x^2-x+4`, we know that `f(x)` is another way of writing `y`, so, `f(x)=y=x^2-x+4` and at `x=2`, we have, `y=(2)^2-2+4=>y=6`

Now, to write our equation, all we have to do is to find `b` from `y=mx+b` (with `y=6, m=3` and `x=2`)

`y=mx+b=>6=3(2)+b=>b=0`

Therefore, our equation will be `y=3x`

Hope this helps and please guys, let me know if I did it wrong.

Thank you :)