Question

What is the slope of the tangent line through (3,2) and (x,y) for x=-2 and y=x3

Answer 1

First you must derive the equation to find the slope:
y = x ^ 3
y '= 3x ^ 2
Then, for x = -2 we have the slope is:
y '(- 2) = 3 (-2) ^ 2 = 12
Then the equation of the line with slope equal to 12 and passing through point (3,2) is:
y = 12 (x-3) +2