3) Find the equation of the tangent line to y=x[squared] - 2 at the point where x=2

My solution:

slope: (change in y over change in x)

f(x) - f(2)

----------

x-2

which after substitution equals

x[squared]-4

------------

x-2

Factor and cancel out to leave [x+2]

Then find slope at [2]

lim[x->2] = 2+2 = 4

Now, find equation:

y-y0 = m(x-x0)

f(x)-f(2) = m (x-2)

x[squared] - 4 = 4(x-2)

x[squared]-4x+4

Equation is x[squared]-4x+4