SOLUTION: The graph of the function y=-x^2 + px + 11 has a tangent when x=2. The tangent passes through the point (4, -9) which is not on the curve. Find the value of p and therefore the eq

Question 1048776: The graph of the function y=-x^2 + px + 11 has a tangent when x=2. The tangent passes through the point (4, -9) which is not on the curve.
Find the value of p and therefore the equation of the tangent.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
The point of tangency is (2, 2p+7). (Why?)
The derivative is given by y' = -2x+p.
At x=2, the slope of the tangent line is thus -2*2+p = p - 4.
Hence, the slope of the tangent line passing through (2, 2p+7) and (4,-9) should satisfy the equation

<===> 8 - 2p = 2p+16 ====> -8 = 4p ====> p = -2.
===> the slope of the tangent line is -6, and the equation of the tangent line is
y--9 = -6(x-4), or y = -6x + 15.
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