Carl_M said:The Attempt at a Solution
Would I just find f'(x) = 2x?
The process for finding k values for tangency involves setting the equations y=kx-2 and f(x) = x^2 equal to each other, solving for x, and then substituting that value of x into either equation to solve for the corresponding value of k.
Yes, it is possible for more than one k value to result in tangency between the two equations. This is because there can be multiple points where the two curves intersect and have the same slope.
The k value represents the slope of the tangent line where the two curves intersect. It is the rate of change of the line at that specific point.
Yes, there are restrictions on the k value in order for tangency to occur. The k value cannot be equal to zero, as that would result in a horizontal line which does not intersect with the parabola. Additionally, the k value cannot be equal to 1, as that would result in the two equations being identical and not intersecting at all.
Yes, a graphing calculator can be used to find the k values by graphing the two equations and finding the points of intersection. However, it is important to also understand the mathematical process for finding k values in case a calculator is not available.