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The value range of the slope of the tangent at any point P on y = 2x ^ 3-radical 3x + 2
K = y '= 6x ^ 2-radical 3
So - root 3
M is the point in the first quadrant of the parabola C: y ^ 2 = 2px (P > 0), and F is the focus of C. if the slope of the straight line MF is the root sign 3, the tangent line segment
M is the point in the first quadrant of the parabola C: y ^ 2 = 2px (P > 0), and F is the focus of C. if the slope of the line MF is root 3 and the abscissa of the midpoint of the line MF is 2, then p=————
The coordinate of point m is (x, √ 2px), and the coordinate of point F is (P / 2,0)
Then KMF = (0 - √ 2px) / [(P / 2) - x] = (√ 2px) / [x - (P / 2)] = √ 3
∵ the abscissa of the midpoint of the segment MF is 2
∴[x+(p/2)]/2=2.②
According to formula (1) and (2), we can find that P = 2 or P = 6
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