Question #f094e

1 Answer
Oct 15, 2017

y = 10x - 14

Explanation:

To find the equation of a tangent line we need both a point of tangency (which we have at (2,6)) and a slope. We can use the first derivative to find the slope of the equation given, which will be the same slope for the tangent line.

dy/dx = 3x^2-2

Using the x value of 2 given:

3(2)^2-2 = 3*4-2 = 12-2 = 10

Now we can use the Point-Slope form of a line to derive the tangent line:

y - y_1 = m(x-x_1)

y - 6 = 10(x - 2)

y - 6 = 10x - 20

y = 10x - 14

graph{(x^3-2x +2-y)(10x-14-y) = 0 [-1, 3, -2, 11]}