(a) find the slope m of the tangent to the curve y = 5 + 5x2 − 2x3 at the point where x =a. m = (b) find equations of the tangent lines at the points (1, 8) and (2, 9). y(x) = (at the point (1, 8)) y(x) = (at the point (2, 9))

a) The slope at (1, 8) is 4.
  The slope at (2, 9) is -4.
These values are computed numerically by the graphing calculator and shown in the column f'(x) in the graphic.

The derivative is y' = 10x -6x². At x=1, y' = 10-6 = 4; at x=2, y' = 20-24 = -4.


b) In point-slope form, the equations of the tangent lines are shown in the graphic.