Anyone know how to do this problem?

Question

mony01 · Answer

attachment

anonymous · Answer

One approach is to roughly numerically integrate f(x) to get F(x).
Look at the areas contributing to f(x) dx  and where they   are
positive and negative. You may not need to be exact.

marsxtc · Answer

If you could hand me a less zoomed in picture, I'll gladly help

mony01 · Answer

is this better @marsxtc

marsxtc · Answer

Nope, but I'll still try give me a second.

marsxtc · Answer

So for the first question at F(3), is it negative or 0? F(3) means that x = 3. So what is it at that point

marsxtc · Answer

It should be neither because the point is at 0 , for both 3 and -3

marsxtc · Answer

Local maxima = kind of like the vertex of a concave up or down function

mony01 · Answer

is the local maxima 2

marsxtc · Answer

The local maxima is at y=2, but only at x= 0. So it should be F(0)

mony01 · Answer

so for the first two questions a and b is neither and for c is 0?

marsxtc · Answer

C is F(0) when its at its maximum.

marsxtc · Answer

Don't write c is 0, you have to be clear! You can even write (0,2) is its maximum

mony01 · Answer

how would i solve the inflection points?

marsxtc · Answer

Inflection points are defined as points when the concavity changes. So when something is Concave up, and it becomes concave down, thats the point of inflection.

marsxtc · Answer

http://mathsfirst.massey.ac.nz/Calculus/Sign2ndDer/images/cost.png Something like that, where its originally concave down and becomes concave up.

mony01 · Answer

so i didn't need to use the integral at all?

campbell_st · Answer

well the zeros of f(x) and the max and mins F(x)

the max and mins of f(x) are the points of inflexion of F(x) 

so that the starting point... so to speak...

marsxtc · Answer

Not all max's/mins are point of inflections I thought?

campbell_st · Answer

ok... what could they be...?

campbell_st · Answer

well here is an example 

hope it helps

marsxtc · Answer

I thought that only applied to second derivatives?

marsxtc · Answer

Not second * but first. And his questions are referring to the graph given not the derivative of it

campbell_st · Answer

well think about the fact the the values of the 1st derivative that allow it to equal zero  are the stationary points max min horizontal points of inflexion... 

so the roots or the 1st derivative are the stationary points

same applies to the 2nd derivative

the max and min are from the 1st derivative are the zeros of the 2nd derivative

hopefully the graph helps to explain it

campbell_st · Answer

the graph given is the 1st derivative... 

f(x)     and you are being asked to coment of F(x)

if F(x) is the function... then f(x) is the 1st derivative...

marsxtc · Answer

Hm, but its just asking simply on what the graph shows, not what the graph implies about the first derivative, does it not?

campbell_st · Answer

well if you think about what the 1st derivative is, then you can comment on F(x) 

as an example... F(-3)

this is a maximum... as the slope the the curve f(x) to the left of -3 is positive... then gets to x = -3 and the slope is zero.... then to the right of -3 the slope is negative

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