Question

find all inflection points of f(x) = 6x^4+58x^3-30x^2+15...

I can find second derivative and get 0, 1/6 for x values that make f"(x)=0...Whered I go wrong?

Answer 1

That 1/6 is right, but not the 0. What's your equation for the second derivative?

Answer 2

72x^2+348x-60, right?

Answer 3

Yeah, that's right. Did you check to see if your signs are correct?

Answer 4

they seem to be.

Answer 5

how do you factor that

Answer 6

First, simplify as much as possible. Divide by 4 and you get 18 x^2+87 x-15

Answer 7

I totally need to work on my factoring/simplification! :(

Answer 8

Just try to see what you can divide all numbers by. Start with something small, like 2. Then do it over and over again until you can't anymore.

Answer 9

couldnt we just divide by 12?

Answer 10

Yes.

Answer 11

Tell me what you get.

Answer 12

6x^2 +29x-5 --> Groups down to (6x^2+30x)-(x+5)

Answer 13

Or (6x-1)(x+5).

Answer 14

Ok, thanks! How about a few mean value problems Ive had the same issues with?

Answer 15

I'm not sure if I remember those. :P

Answer 16

2x^3-15x^2-36x+2 AVG Slope= 56
f' = 6x^2-30x-36
need to find values of x for f'=56. Pretty sure its a factoring thing

Answer 17

[-6,10]

Answer 18

So, 56=6x^2-30x-36?
0=6x^2-30x-92.
hmmm.... I think you might need the quadratic formula for this.

Answer 19

yup. didnt even think of bringin the 56 over...

Answer 20

Always make sure a 0 is on one side, if possible, when doing problems like these.

Answer 21

7.145786622,-2.145786622?

Answer 22

Yup.

Answer 23

nice! appreciate it! I understand most of the material, but get stuck with these very basic skills, somehow....

Answer 24

That's understandable. That describes how most of my classmates were when I took Calculus. :P

Answer 25

How about this one. 6sqrtx+1, f' = 3x^(-1/2). M= 1.34846923. interval [4,6]

Answer 26

3/\[\sqrt{x}\]=1.34846923

Answer 27

3/√x= 1.34846923
3= 1.34846923√x
9= 1.34846923^2 x
9/(1.34846923^2)= x

Answer 28

Ok. f'=6x^2-3 M=47. [-5,5].. I get sqrt8.333333333, but is wrong, clearly.

Answer 29

is b=0 for this?

Answer 30

Yeah.

Answer 31

2.886751346 and its negative counterpart, right? As long as they are within the given interval, I thinkith.

Answer 32

Yup.

Answer 33

stuck here: 1/x^2=.0277777778

Answer 34

x=1/sqrt.0277777778?

Answer 35

...Sorry to question this so late, but are you sure you're using the right methods? 'Cause I've forgotten and I'm just going along with what you're doing.
&yes.

Answer 36

for mean value?

Answer 37

yeah

Answer 38

quick refresher. MVT says there exists an f'(c)=M

Answer 39

the average slope on the given intervals. So, f(b)-f(a)/b-a = f'(c)

Answer 40

Ok, now I remember. Thanks.

Answer 41

How do I add friends on here?

Answer 42

Dunno.