Expert: Ahmed Salami - 3/24/2010

Question
Prove that the line y=x+2 is a tangent to the parabola y=x^2-5x+11.

Answer
Hi Mathu,
The slope of the line y = x + 2 is always 1. If this line is to be a tangent to the curve
y = x² - 5x + 11
then they must both have the same x-y values at the point where the slope of the curve is also 1.
Now, the slope of the curve is given by
dy/dx = 2x - 5
when this is equal to 1
2x - 5 = 1
x = 3
At this point,
y = x + 2 has a value
3 + 2 = 5
y = x² - 5x + 11 has a value
(3)² - 5(3) + 11 = 9 - 15 + 11
                = 5
The line and curve both have the same y values and so we have our proof.

Regards