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 (x-1) is a factor, so by synthetic division I found

x^3 + x - 2 = 0

(x-1)(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

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