Question

How do you find the equation of the line tangent to the graph of `y=x^2` at x=2?

Answer 1

I found: `y=4x-4`

Explanation:

First you need the slope `m` of the tangent. You find it evaluating the derivative of your function in `x=2`:
`y'=2x`
so `m=y'(2)=2*2=4` this is the slope of the tangent at the point of coordinates:
`x_0=2` and `y_0=x^2=2^2=4`;
now you can use the relationship:
`y-y_0=m(x-x_0)`
`y-4=4(x-2)` rearranging:
`y=4x-8+4`
`y=4x-4`

Graphically: