Posted by **Allison** on Wednesday, August 17, 2011 at 9:05pm.

Show that the tangent line to the curve y=x^3 at the point x=a also hits the curve at the point x=-2a.

Any help?! PLEASE!

- calculus!URGENT -
**Reiny**, Wednesday, August 17, 2011 at 9:23pm
dy/dx = 3x^2

at x=a , y = x^3 and dy/dx = 3a^2

equation of tangent:

y = 3a^2x + b

but (a,a^3) is on it, so

a^3 = 3a^2(a) + b

b = -2a^3

tangent equation: y = (3a^2)x - 2a^3

intersect that line with y = x^3

x^3 = 3a^2x - 2a^3

x^3 - 3a^2x + 2a^3 = 0

We already know that x-a is a factor, since x=a is a solution.

so it factors to

(x-a)(x^2 + ax - 2a^2) = 0

(x-a)(x-a)(x - 2a) = 0

so x=a, or x=a, or x = 2a

- calculus!URGENT -
**Reiny**, Wednesday, August 17, 2011 at 9:25pm
second line should have been ----

at x=a , y = x^3 and dy/dx = 3a^2

- calculus!URGENT -
**Allison**, Wednesday, August 17, 2011 at 9:47pm
thank you soooooo much!

## Answer this Question

## Related Questions

- calculus - Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show ...
- 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 - Damon - Find the line which passes through the point (0, 1/4) and is ...
- 12th Grade Calculus - 1. a.) Find an equation for the line perpendicular to the ...
- AP Calculus - Consider the curve given by x^2+4y^2=7+3xy a) Show that dy/dx=(3y-...
- Calc AB - Suppose that f(x) is an invertible function (that is, has an inverse ...
- calculus - 1. Given the curve a. Find an expression for the slope of the curve ...
- math - consider the curve defined by the equation y=a(x^2)+bx+c. Take a point(h,...
- please help; calc - original curve: 2y^3+6(x^2)y-12x^2+6y=1 dy/dx=(4x-2xy)/(x^2+...

More Related Questions