given a graph how do you identify intervals on which f''(x) < 0

- anonymous

given a graph how do you identify intervals on which f''(x) < 0

- katieb

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- anonymous

this is a second derivative.

- anonymous

yes

- anonymous

im looking at a graph however, i dont know how to calculate the intervals on which f''(x) <0

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- anonymous

is this an ad?

- anonymous

from sammi i think so. i cant afford to pay for help

- anonymous

im just trying to get help on my homework

- anonymous

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- anonymous

yeah sammi but it cost

- anonymous

you can earn money by answering questions there too!

- anonymous

accordingly there are people who pay the money.

- anonymous

anyway ken could you help me figure this problem out?

- anonymous

you can do the first derivative , and then do the second.

- anonymous

for example, suppose f(x)=x^3+6x^2+4x+3
then f'(x)=3x^2+12x+4
f''(x)=6x+12

- anonymous

how to i find the first der. from the graph

- anonymous

If you have a graph of f, you look at the places on the graph where the concavity is negative (curve opens downward). This will be the places where the second derivative is negative.

- anonymous

back up a little bit, do you know the basic derivatives?

- anonymous

polpak is right, but it is just perceiving by eyes, not calculating

- anonymous

if i have numbers i can find der., but there is only letters

- anonymous

to see where the first derivative is negative you look to see where the slope of the tangent to the graph points downward as x moves positively..

- anonymous

it's the same.

- anonymous

im not understanding

- anonymous

f'(x) stands for the slope of the tangent line at (x,f(x)).
f''(x) stands for the change of the slope.

- anonymous

I presume you have some graph of a function, and you need to identify where the second derivative of the function is less than 0

- anonymous

i do have a graph so where it is sloping below 0

- anonymous

Is the graph of f, or of f'' ?

- anonymous

suppose f(x)=ax^3+bx^2+cx+d
then f'(x)=3ax^2+2bx+c
then f''(x)=6ax+2b

- anonymous

f'(x)

- anonymous

If it's the graph of f' then you simply need to see where the tangent lines have negative slope to find where f'' is less than 0.

- anonymous

i don get ya.(><)

- anonymous

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