Point A and B lie on the curve #y=x^2-4x+7#. Point A has coordinates #(4,7)# and B is the stationary point of the curve. The equation of a line L is y=mx-2 Where m is a constant. In the case where L passes through the midpoint of AB find the value of m?
3 Answers
Explanation:
At the stationary point,
The corresponding
Given that,
Enjoy Maths.!
Explanation:
The function will have a stationary point when
#dy/dx= 2x - 4#
So
#0 = 2x -4 -> 4 = 2x -> x = 2#
The corresponding value of
We now must find the midpoint between
#M = ((2 + 4)/2, (3 + 7)/2) = (3, 5)#
We can now effectively solve for
#5 = 3m - 2#
#m = 7/3#
Hopefully this helps!
Explanation:
To find the stationary point,
We can find the x-coordinate of the stationary point,
Find the corresponding y value by evaluating the function at
Point
The midpoint between
Substitute the point