The curve y=x^33x^28x+4 has tangent L at point P (1,8). Given that the Line M is parallel to L and is also a tangent to Q show that the shortest distance between L and M is 16 root 2
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1 answer

y' = 3x^2  6x  8
at (1,8), y' = 3  6  8 = 11
So at Q, the slope of the tangent must also be 11
3x^2  6x 8 = 11
3x^2  6x + 3 = 0
x^2  2x + 1 = 0
(x1)^2 = 0
x = 1
mmmhhh, expecting two values of x
y'' = 6x6
= 0 for point of inflection
x = 1
if x = 1, y = 138+4 = 6
ahhh, found the problem.
you said that there was a tangent at (1, 8), but that point does not lie on the curve
There is a typo, or the question is bogus. 👍
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answered by Reiny
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