Question

Find the absolute minimum of the function of f(x) = 3 x^2 - 10 x + 6, in the interval 0 is less than or equal to x and x is less than or equal to 8.

Answer 1

can you find the derivative?

Answer 2

\[f \prime(x)=6x-10\]

Answer 3

set that equal to 0 and solve for x

Answer 4

this is a upward opening parabola, so the min is the vertex...

Answer 5

x= -10/6

Answer 6

why -?

Answer 7

i meant 10/6 whooopsie

Answer 8

yep

Answer 9

would that be the min?

Answer 10

do you know how to find the vertex of a parabola?

Answer 11

-b/(2a)

Answer 12

yes its a min

Answer 13

that ended up being wrong.

Answer 14

its not, its the only min....

Answer 15

its the vertex

Answer 16

-b/(2a) = 10/6

Answer 17

huh? so how do I find the absolute min?

Answer 18

same thing

Answer 19

think of what a parabola looks like

Answer 20

its smallest value is the vertex right?

Answer 21

this is also where it has a slope = 0

Answer 22

so there are two ways to find the max/min of a parabola

Answer 23

put x = 10/6 in f(x) = 3x^2-10x+6

Answer 24

yes you found where its min is, you need to plug that back into f(x) to get the value

Answer 25

you found the x coordinate...

Answer 26

i got -2.3333333 and it ended up wrong again.. @zzr0ck3r

Answer 27

don't round

Answer 28

-7/3

Answer 29

ohhhh okay. I got it!!! (: thank you so much! @zzr0ck3r

Answer 30

np