Question

Find an equation of the tangent line at the indicated point on the graph of the function
w = g(z) = z2 - 3, (z, w) = (3, 6)

Answer 1

w = g(z) = z^2 -3, (z.w) = (3,6)

Answer 2

The derivative represents the rate of change at a particular function. Take the derivative g(z) = z^2 - 3 to find g'(z) = 2z. To find the slope of the tangent line at that function put the z value into the derivative g'(3) = 2*3 = 6. The slope of the tangent line is 6. m = 6, and you have a point (3, 6), so you can put this into the point slope form of the line: z - z1 = m(w - w1)

z - 3 = 6(w - 6)

Answer 3

Screwed up on the definition, the derivative represents the rate of change at a particular POINT, not function.