Using mean value theorem,prove that there is a point on the curve y=2x2−5x+3 between the points A(1,0) and B(2,1)where tangent is parallel to chord AB. Also find the point.
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sorry but I didn't understood the question.
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The point is (1.5, 0)
Proof:
The given curve is
or,
The slope of the curve is given by
or,
or,
Now, by mean value theorem, there exists a point between (1, 0) and (2, 1) where
Thus
That means at point x = c, the slope must be 1
Thus
or,
Clearly x = 1.5 lies between x = 1 and x = 2
At x = 1.5
Thus the point is (1.5, 0) which lies between (1, 0) and (2, 1)[/tex]
Hope this answer is helpful.
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