Posted by Laura on Sunday, January 4, 2009 at 2:58pm.
The curve f(x)=x^4+2x^2+x has a tangent at the point (1,2). Is this line tangent to the curve at another point and, if so where?

Calculus  Reiny, Sunday, January 4, 2009 at 3:18pm
dy/dx = 4x^3 + 4x + 1
so at (1,2) dy/dx = 4+4+1 = 9
so is 4x^3 + 4x + 1 = 9 ?
x^3 + x  2 = 0
we already know that (x1) is a factor, so by synthetic division I found
x^3 + x  2 = 0
(x1)(x^2 + x + 2) = 0
x = 1, we knew that or
x = (1±√7)/2 which is not real
so there are no other points where the tangent has a slope of 9 
Calculus  BOB, Sunday, January 4, 2009 at 4:35pm
find the tangent line, graph both of them