Question

Help with a math problem?

Answer 1

the tangent line occurs at the vertex of the this particular function which happens to be a parabola

Answer 2

Okay so first I would have to derive my equation right?

Answer 3

Correct^

Answer 4

So I would get 9x-3 and then what would I do?

Answer 5

Well from there...you want a tangent line that is horizontal...and since a tangent line is the slope at any given point...that would mean the slope would be 0 right?

So if we have the derivative of the function...we need to find where the derivative = 0

Answer 6

So it would be -3 at 0

Answer 7

No I mean we have the derivative...and we want the derivative to equal 0

\[\large 9x - 3 = 0\]

solve for 'x' :)

Answer 8

Oh my bad to it would be 3/9.

Answer 9

Mmhmm...or 1/3 right :P

So that means that at x = 1/3 ...we will have a horizontal tangent line

Answer 10

And if I wanted to find the equation for the tangent line at 2 would i just plug in 2 into my derived equation?

Answer 11

But we probably should figure out where that will be in terms of 'y' now...

So plug in your x = 1/3 into your original equation and solve for 'y'

Answer 12

I got 1.5

Answer 13

Good...so just to finish up the first question

At (1/3 , 1.5) there will be a horizontal tangent line

Answer 14

And as far as your second question...yes you would just plug in x = 2 and solve for y in your derived ezpression

Answer 15

Cant spell apparently >.<

"expression"

Answer 16

Okay thank you so much!

Answer 17

No problem! :)