Homework Help: Calculus

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 = (-1ą√-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

Answer this Question

Related Questions

Calculus - Consider line segments which are tangent to a point on the right ...
calculus - Consider line segments which are tangent to a point on the right half...
calculus - Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show ...
Help Calc.! - original curve: 2y^3+6(x^2)y-12x^2+6y=1 dy/dx=(4x-2xy)/(x^2+y^2+1...
please help; calc - original curve: 2y^3+6(x^2)y-12x^2+6y=1 dy/dx=(4x-2xy)/(x^2+...
calculus - 1. Given the curve a. Find an expression for the slope of the curve ...
12th Grade Calculus - 1. a.) Find an equation for the line perpendicular to the ...
Calculus - If a tangent line is drawn to the parabola y = 3 - x^2 at any point ...
calculus - If a tangent line is drawn to the parabola y = 3 - x^2 at any point ...
Calculus - the curve: (x)(y^2)-(x^3)(y)=6 (dy/dx)=(3(x^2)y-(y^2))/(2xy-(x^3)) a...

For Further Reading

First Name:
School Subject:
Answer: