Asked by kailey

hello! i just needed help to verify or falsify my answer and any explanation as to why would be extremely helpful! thanks ahead of time.

y=(x^2)-6x+10
a. at x=3
b. at x=0
c. at x=1
d. at x=-3

my answer was D.

thanks again!
Answered by kailey
just realized i didn't even specify the directions, haha. it states 'Find the horizontal tangents of the curve.'
Answered by Damon
Huh?
There are values of y for each of those values of x

at x = -3
y = 9 + 18 + 10 = 37

at x = 3
y = 9 -18 + 10 = 1

what is the question?
Answered by Damon
Oh
y' = 2x-6
for 0, x = 3
Answered by kailey
Yeah, i did forget to include that. I put it in a comment above though! Thanks again and sorry about that. 'Find the horizontal tangents of the curve."
Answered by Damon
You do not really need calculus. It is a parabola, find the vertex
y=(x^2)-6x+10

x^2 - 6 x = y - 10

x^2 - 6 x - 9 = y-19

(x-3)^2 = (y-19)

vertex at (3 , 19)
Answered by kailey
thank you!!

also had another quick question. when something asks for y'', is there a name for that type of derivative? like what does y'' mean? thanks again. sorry for having so many questions.
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