Find the value of k if the line y = x + k is tangent to the graph of y = x^2.
The slope of y = x + k is 1.
We need to find where the slope of y = x2 is 1.
Find the first derivative of y: y' = 2x This formula will give us the slope of y = x2 at every point.
When does 2x = 1? ---> x = 1/2.
So, when x = 1/2, the slope of y = x2 is 1.
When x = 1/2, y = x2 ---> y = (1/2)2 = 1/4.
So the point of intersection of the line and the parabola is the point (1/2, 1/4).
The equation of the line will be: y - 1/4 = 1(x - 1/2) ---> y = x - 1/4