Question

Question #f094e

Answer 1

`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]}