Question

hi i need help please im trying to use the quadratic formula to solve 3x^2-2x+4 thank you

Answer 1

is this using the b^2-4ac/2a

Answer 2

\[x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\]

Answer 3

You have a=3, b=2, and c=4

Answer 4

i did it that way and then when i tried to find F(x)=0 i do not get it right

Answer 5

b=-2 not 2

Answer 6

Inside the square root sign, you get\[2^2-4(3)(4)<0\]You can't take the square root of a negative number, which means there are no (real) solutions to this equation.

Answer 7

agreed

Answer 8

well i took the square root of 4 and then of 48 the i subtracted

Answer 9

yes is would be sqrt(-44)/6 and you cant get a square root of a negative number

Answer 10

That violates order of operations. You have to do the 4-48 first.

Answer 11

if i have f(x)=x^3-x^2+4x-3 f'(x)=3x^2-2x+4 right

Answer 12

Yep.

Answer 13

from that i have to find the intervals of increase and decrease and i cant. Im not sure if the function is wrong

Answer 14

Oh, I see. This means that it doesn't switch from negative to positive or vice versa. The parabola opens upward and does not have a zero, which means that every value is always positive.
This implies that the function is increasing from -infinity to infinity.

Answer 15

You can also look at the graph to see this visually.

Answer 16

What does the question actually say?

Answer 17

the question says: for the function f(x)=x^3-x^2+4x-3 determine the intervals of increase and decrease, location of maximum and minimum points, intervals concavity up or down and location of points of inflection

Answer 18

The fact that the derivative never equals zero means that it is monotonic (always increasing or decreasing - increasing in this case) and that there are no max or min points.

Answer 19

Do you know about the second derivative?

Answer 20

This question is basically asking u to investigate the behavior of the function.

There are different methods for doing that, you have tried the first derivative and jabberwock has explained what that result means.

The secon derivative tests for concavity, points of inflection but first u need to have an idea about the general shape of the function.

You could do this by calculating simple test points for instance (-1,0 and -1 are good candidates to start with).

Answer 21

the second derivative would be 6x-2 right?

Answer 22

Yes.

Answer 23

Yes. You can use this to test what's going on with the function.

Answer 24

but since this function is always increasing there is not concavity or point of inflection right?

Answer 25

There is. The concavity changes from positive to negative. Look for where...
\[0=6x-2\]to see where the points of inflection are

\[0>6x-2\]to see where it's concave down

\[0<6x-2\]to see where it's concave up

Answer 26

This is why I said you have to do test points first (a rough plot, perhaps) in order to know a bit about what is going on before u apply the tests.

Answer 27

so the function is concave up when \[x >1/6\] and concave down when \[x <1/6\]

Answer 28

Yes, if you look at the graph here, I think you can just about see it.

http://www.wolframalpha.com/input/?i=x^3-x^2%2B4x-3

Answer 29

THANK YOU so much

Answer 30

I have another question please if somebody can help me

a function has a local maximum at x=-2 and x=6 and a local minimum at x=1
what is this information telling about the function?

Answer 31

Assuming these are all these are the only extrema and the function is continuous, we know that the function is decreasing on the interval (-2, 1) and is decreasing on the interval (1, 6)

Answer 32

If it is a differentiable function, we know that f'(-2)=0. It's the same with f'(6) and f'(1).

Answer 33

would it be odd or even?

Answer 34

Neither.

Answer 35

and it would be a polynomial of 4th degree right

Answer 36

You really can't say from this information. For instance, some cubic equations can have a maximum and a minimum, but some (like y=x^3) don't have a maximum or a minimum.

Answer 37

It could be of the 4th degree, 6th degree, etc. Or, if it's not differentiable, you can't tell at all.

Answer 38

but it can be smaller than 4th?