Question

What is the slope of the tangent line through (0,-3) and (x,y) for y = 3x2 - 3 and x=1?

Answer 1

First you must derive the equation to find the slope:
y = 3x ^ 2 - 3
y '= 6x
Then, for x = 1 we have the slope is:
y '(1) = 6 (1) = 6
Then the equation of the line with slope equal to 6 and passing through point (0, -3) is:
y = 6x - 3
The slope is m = 6