Question

What is tangent to `y = x^2` when x = 2?

Answer 1

You start by evaluating the derivative at `x=2`:
`y'(x)=2x`
at `x=2`
`y'(2)=4` which represents the SLOPE of the tangent;
then use `y-y_0=m(x-x_0)`
to find the equation of the tangent, where:
`x_0=2`
`y_0=2^2=4`
`m=slope=4`
So you get:
`y-4=4(x-2)`
`y=4x-4`