Tangent lines to cubic with given slope: Find the equations of the tangent lines to  where the slope is 10.

The slope of the desired lines will be 10 at the desired points  and will equal the derivative of the function y at that point. At any point,

and at x_T we have 

Solving, we get , or .

To get the y coordinates, we substitute these values of x into the original equation:

At x_T = 2, we get 

At x_T = -2, we get 

Consequently, the points of tangency are (2,4) and (-2,-4).

The tangent lines are each described in the slope intercept form as .

We can substitute the coordinates of each point to solve for the value of b for that line:

At (2,4) we have , or b = -16. The line here, then, is 

At (-2,-4) we have , or b = 16. The line here, then, is 

Try to draw a graph of this information. Then check your graph.