Implicit Differentiation - Tangent Line & Horizontal Tangents

[Pondera]

Homework Statement

Find an equation of the tangent line to this curve at the point (1, -2).

Homework Equations

The Attempt at a Solution

2y' = 3x^2+6x
y' = 3x^2+6x
y'=3/2x^2+3x

y+2=3(x-1)
y+2=3x-3
y=3x-5

 

[lanedance]

Hi Pondera

Homework Statement

Homework Equations

The Attempt at a Solution

2y' = 3x^2+6x
y' = 3x^2+6x

where did the 2 go?

y'=3/2x+3x

where did the power of x go?

y+2=3(x-1)
y+2=3x-3
y=3x-5

I think the arithmetic needs a little work

 

[Pondera]

Lane, I divided 3x^2+6x by two and got y'=3/2x^2+3x.

By power of x, I take it you mean power of 2? I neglected to put that in here, but it is on my scratch paper, I appologize.

I don't see where the arithmetic is flawed? I certainly believe that that is likely not the equation/form that I need, but I believe I worked what I figured to be correct out correctly. Can you be more specific?

 

[lanedance]

ok I don't really understand what you are trying to do, just picked up some misssing parts as discussed

the question is clipped off when I veiw it

 

[lanedance]

Also the implict derivative w.r.t. x of y² is not 2y', it will be:

$$\frac{d}{dx} y^2 = 2y \frac{dy}{dx}$$

horizontal derivatives where y' = 0