(a) find the slope m of the tangent to the curve y = 5 + 5x2 − 2x3 at the point where x =
1 answer:
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.
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.
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