Posted by Dom on Monday, October 18, 2010 at 2:21pm.
Find the number c if the line y=x is to be tangent to the graph of f(x)=x^4+c. what are the coordinates of the points of tangency?

calculus  Reiny, Monday, October 18, 2010 at 3:49pm
so x = x^2 + c
x^2  x + c = 0 must have only one root, that is,
the discriminant must be zero
b^2  4ac = 0
1  4(1)(c) = 0
c = 1/4
so x^2 x + 1/4 = 0
(x 1/2)^2 = 0
x = 1/2
then y = 1/2
the point is (1/2,1/2)
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