Question

How do I find a horizontal tangent? (Calc 1)

Answer 1

Lets say I have\[f(x)=x^3+3x^2+3x^2+3\]
I know that the slope is 0, and I can derive, but how do I find y1 or x1 ?

Answer 2

@eliassaab, @ganeshie8

Answer 3

first derivative at a point gives you the slope of tangent at that point

Answer 4

and you know that the slope of a horizontal tangent is 0

Answer 5

start by finding the derivative, set it equal to 0 and solve x

Answer 6

whats the derivative of f(x) ?

Answer 7

\[\frac{d}{dx} (x^3+3x^2+3x+3)=3x^2+6x+3\]\[0=3x^2+6x+3=3(x^2+2x+1)=3(x+1)^2~~~~->~~~~x=-1\]

Answer 8

So, since the x-coordinate is -1, then I know the y-coordinate.
\[(-1)^3+3(-1)^2+3(-1)+3\]\[-1+3-3+3\]\[-1+3\]\[y_1=2\]

Answer 9

\[y-y_1=0(x-x_1)\]\[y-2=0\]\[y=2~~~(answer)\]

Answer 10

Yes, tnx that makes sense,
https://www.desmos.com/calculator/lye8nzzwlv

Appreciate it

Answer 11

Excellent !

Answer 12

your job is indeed is excellent.

Answer 13

Just what I needed.

Answer 14

And thus the vertical tangent would be x=-1,
(setting a vertical line through the point)

Answer 15

Tnx once again:) Have a good day sir:)

Answer 16

no vertical tangents

Answer 17

Why not?

Answer 18

we only have one horizontal tangent y = 2
thats all

Answer 19

Ohh true dat:)

Answer 20

it's +- infinity depending on whether it is going up or down.

Answer 21

a vertical tangent looks like this :

Answer 22

So a vertical tangent can only be, when the curve itself isn't a function?

Answer 23

yes the slope is infinity for a vertical tangent

Answer 24

thats a good question

Answer 25

you can get vertical tangent for functions also

Answer 26

let me think of one..

Answer 27

not really, because that means that the slope of the function is undefined, i.e. more than 1 point on the same y value.

Answer 28

(I think)