Finding k Values for Tangency of y=kx-2 and f(x) = x^2

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SUMMARY

The discussion focuses on determining the values of k for which the line y = kx - 2 is tangent to the parabola f(x) = x^2. The derivative of the function, f'(x) = 2x, is essential for finding the slope at the point of tangency. The key insight is that the line and the parabola must intersect at exactly one point, which can be established by applying the condition for equal roots in the quadratic formula. This leads to a specific quadratic equation that can be solved to find the required k values.

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Carl_M
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Homework Statement


For what values of k is the line y = kx - 2 tangent to the graph of f(x) = x^2?


Homework Equations





The Attempt at a Solution



Would I just find f'(x) = 2x?
 
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Carl_M said:

The Attempt at a Solution



Would I just find f'(x) = 2x?

No but solving y=kx-2 and y=x2 would yield only one solution for x

Hint: recall the condition in the quadratic equation formula for equal roots.
 

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