Question

can someone help me find the critical points for: .288x2 +3.47x +5.46?

Answer 1

f' = .288(2)x +3.47 solve for f'=0

x = -3.47/(.288(2))

Answer 2

actually its even simpler than that, only one critical point exists because this graph looks like a "U". The critical point is at the bottom part of th "U"

Answer 3

its not multiplied by 2 thats supposed to be a power...sorry typo

Answer 4

-3.47/[2(.288)] comes out the same, but you aint gotta try to derive it :)

Answer 5

right, I assumed that

Answer 6

is a critical point a coordinate?

Answer 7

6.024 is pretty close,

it is the "x" coordinate; just plug it into the equation to get the "y" coordinate.

Answer 8

the x coordinate is -6, so I plug this in to the original equation?

Answer 9

(6.024,36.81) is what I get for a coordinate if I did it right :)

Answer 10

yeah.... -6... which means I plugged it in wring ...

Answer 11

wait can you tell me how you did that?

Answer 12

which part?

Answer 13

do you know how to find a derivative?

Answer 14

how you find the coordinate? and is that coordinate the critical point?

Answer 15

to find which value of x gets us a critical point, we can find the derivative of an equation if you do not know what the graph of the equation will look like

Answer 16

y =.288x^2 +3.47x + 5.46

the derivative is gotten thru using the rules for derivatives, mainly the power rule for this equation.

Answer 17

the power rule states:

when ever you have a variable to the power of a number like:

x^4

you can multiply the power by whatever number is in front of the "x" and then reduce the power by 1

(4) x ^ 4-1 = 4x^3

does that make sense?

Answer 18

yes...then what?

Answer 19

y =.288x^2 +3.47x + 5.46

y' = (2).288x^1 + (1)3.47x^0

y' = .165888 x + 3.47

when y' = 0 we have found a critical point for "x". so we set y' = 0

0 = .165888x + 3.47

solve for "x"

-3.47/.165888 = x this is the value of x that we need to use in the original equation; the y = .288x^2 +3.47x +5.46

Answer 20

and I messed up that 2(.288).... redo that will ya :)

Answer 21

x = -3.47/.576 which is about -6

Answer 22

ok thanks! could the critical point and the minimum point be the same?