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I am having extreme trouble with this differentiation problem. It says, "Find k such that the line is tangent to the graph of the function."
F(x) = x^2 - kx
y = 4x - 9
I don't understand the step where you set f(x) to equal y. How do you get rid of the k?
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Fermat, prior to Newton and Leibniz, had a method for problems like this. It uses the fact that a tangent line has a "second order" intersection with a curve. That is, if f(x) is tangent to t(x) at
must be a double root
of f(x)= g(x). Your given curve is
and your desired tangent line is
so we look at the equation
which is the same as
By the quadratic formula, solutions are given by
. There will be a double root if and only if the discriminant,
. Solve that equation for two values of k.
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