Answer:
(1/3(5-√34), 1/27(-205+32√34)) and (1/3(5+√34), 1/27(-205-32√34))
Step-by-step explanation:
The slope of the given line is the x-coefficient, 4. Then you're looking for points on the f(x) curve where f'(x) = 4.
f'(x) = 3x^2 -10x +1 = 4
3x^2 -10x -3 = 0
x = (5 ±√34)/3 . . . . . x-coordinates of tangent points
Substituting these values into f(x), we can find the y-coordinates of the tangent points. The desired tangent points are ...
(1/3(5-√34), 1/27(-205+32√34)) and (1/3(5+√34), 1/27(-205-32√34))
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The graph shows the tangent points and approximate tangent lines.
