Find the coordinates of the point of intersection of the tangents to the graph of y=x^2 at the points at which it meets the line with the equation y=x+2
Answer of this question is = (1/2, -2)
Please Help !!!
Find the coordinates of the point of intersection of the tangents to the graph of y=x^2 at the points at which it meets the line with the equation y=x+2
Answer of this question is = (1/2, -2)
Please Help !!!
To find A and B, set x^2 equal to x + 2 and solve for x.
For each, use the co-ordinate pair and the slope at that point (twice the x-value?) to find the tangent-line equation.
Then set both equations equal...
A small point: suppose x_0 and x_1 are points of intersection. Than you can find functions of tangents as:
$\displaystyle y = (1/f'(x_0))(x-x_0)+f(x_0)$
$\displaystyle y = (1/f'(x_1))(x-x_1)+f(x_1)$
or
$\displaystyle y = (1/(2*x_0))(x-x_0)+x_0^2$
$\displaystyle y = (1/(2*x_1))(x-x_1)+x_1^2$