Answer to Question #203202 in Real Analysis for Rajkumar

Question

Show that on the curve y = 3x² − 7x + 6 the chord joining the points whose abscissa

are x = 1 and x = 2, is parallel to the tangent at the whose abscissa is x= 3/2

Answer 1

Solution

Ordinates for two points of chord abscissa x₁=1 and x₂=2 are y₁=y(x₁)=2 and y₂= y(x₂)=4.

The slope of the chord is k=(y₂-y₁)/(x₂-x₁)=2.

The tangent at the any point of curve y(x) is the line with the slope equal to its derivative y’(x)=6x-7. At the abscissa x₀=3/2 the tangent is y’(3/2)=2.

So slopes of the chord and the tangent are equal. Therefore this lines are parallel.