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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