/sci/ - Science & Math

[sudochan !4x27SV2ZHE No.2991116]

so the ap calc ab test is tomorrow.

can anyone explain why the answer to this problem is (A)

[Anonymous No.2991122]

I don't know but I'm taking calc in the summer so I hope that you get an answer I can use.

[Anonymous No.2991137]

If f''(x) < 0, then f'(x) < 2 for 3<x<4 and f'(x) > 2 for 2<x<3. This means that f(3) - f(2) > 2 and f(4) - f(3) < 2.

[Anonymous No.2991140]

Positive slope, concave down. Median value theorem.

[Anonymous No.2991138]

go to sleep Tom

[Anonymous No.2991145]

f(x) is concave down due to f ''(x) being negative.
If f '(3) is 2, then f '(2) is greater than 2 and therefore f(2) must be less than 3, leaving A and B.
Similarly, f '(4) will be less than 2, so f(2) will be less than 7, leaving A as the only possible choice.

[Anonymous No.2991153]

Woo! Super excited for that test!

As for this problem, the main keys are that that f'(3)=2, and that the second derivative is less than zero (meaning that the original function is concave down, and that the first derivative is decreasing). Using the simple slope equation, and the given slope of 3, The slopes in A are the only one in the set that are decreasing.

[Anonymous No.2991154]

You are able to eliminate B and C since if you take the slope of the values you will not get 2-> f(2) - f(4)/(4-2)= 2. Then you know that the second derivative is less than 0 so that the rates that f is increasing should decrease so the difference between the f values will become smaller and smaller.

[Anonymous No.2991162]

>>2991145
But I'll add that you should be wary, because this question was simplified in that f(3) was 5 for all possible answers.

[Anonymous No.2991180]

Hi, OP. Don't know if you could figure out all the rumbling from above. Basically works like this:
1)Take the derivative of each 'f' at 3. use [f(4)-f(2)]/(4-2)
If it is not '2' than you cant use that.
2)Take the derivative of each 'f' for 2, 3, and 4. Tabulate these values. Then take the derivative of these derivatives, (ie take the 2nd derivative) and tabulate these values.
3)Look for a function that has a negative 2nd derivative at 3. That is the answer.

[Anonymous No.2991189]

Calc BC fag reporting in, just to add my excitement into this thread. Also, for the question you posted, concave down means that the mean value of f'(x) on [2,3] has to be greater than f'(x) on [3,4]. Also, f'(x) must be positive for all values x on [2,4] and the mean value of f'(x) on [2,4] must be 2, from your given values. Answer A is the only given choice that satisfies those three conditions, so it's A.

I'm surprised you're having trouble with this, I'm more sweating over the outlandish integration techniques. To each his own demise, I suppose. Best of luck to you tomorrow, OP and every anon who's taking the exam tomorrow!

[sudochan !4x27SV2ZHE No.2991193]

why can't the answer be (D)

[Anonymous No.2991212]

>>2991193
Because it isn't concave up

[sudochan !4x27SV2ZHE No.2991219]

>>2991180
i don't get what you mean in step 2?

sorry haha

[Anonymous No.2991236]

>>2991212
Answer D shows a mean value for f''(x) of 0 on the interval, so it's not necessarily concave up or concave down over the entire interval. Your reasoning is pretty much right but you'd lose the points on free response or whatever. To be perfectly correct you should have said that the answer has to be concave down, rather than it can't be concave up.

If it makes you feel better, I typed out f"(x) by hitting apostrophe twice instead of just making quotation marks, which is kind of silly.

[sudochan !4x27SV2ZHE No.2991247]

>>2991189

ok i sort of get it. thanks!

[sudochan !4x27SV2ZHE No.2991261]

I'm going to keep this thread for those of you who want to post last minute questions for the AP Calc AB/BC exam tomorrow!

And good luck to all

[Anonymous No.2991271]

is it true that we aren't getting marked off for guessing?

it would be stupid to leave questions blank, but i want to confirm to make sure.

[Anonymous No.2991290]

>>2991271
You heard correct. They will not mark off for guessing. That just means that the scoring guidelines/questions will be harder though, so don't get too pumped. Definitely make sure to guess on everything though.

[Anonymous No.2991305]

>>2991290
>geussing

[Anonymous No.2991312]

>>2991305
>trying to be smug
>misspells the word "guessing"

[Anonymous No.2991344]

>>2991290
does this apply to the other AP exams as well (Physics)

are they going to make the questions more difficult because of this?

[Anonymous No.2991348]

Can someone help me with slope fields/differential equations? My class barely went over them.
Am I right in doing:

I get dy/dx = some equation.
Get all the y's on one side with dy, all the x's on another with dx
Integrate both sides.
Rearrange the equation so I get y = blah blah blah + C.
Plug in a set of values or whatever they ask you.

Also, this question. How the fuck do I do D?

[Anonymous No.2991355]

I am fucked for this exam together, I'll be lucky to pass with a 3.

[Anonymous No.2991357]

>>2991348
whoops, upside down picture.

[Anonymous No.2991389]

>>2991357
Bump.

[Anonymous No.2991408]

>>2991389
bumping for interest. is this AB or BC?

[Anonymous No.2991420]

>>2991408
AB. Thanks for the bump.

[Anonymous No.2991461]

>>2991116
any niggers taking BC? or are all you fags just AB fucks.

[Anonymous No.2991477]

>>2991461
Could you help me?

[Anonymous No.2991485]

sure I'll try, poor ab fag

-love
bc pwner

[Anonymous No.2991490]

>taking AB test also tomorrow
>studied barely anything
>laughing as OP is trying to study at the last minute which will probably just result in memory lost during the test thus lost in points
>mfw when i'll probably get a 3 and deal with it

[Anonymous No.2991505]

ab here,
can someone explain 2nd fundamental theorem of calc as in taking the derivative of an integral with a variable as the upper bound? also, what about integrals of absolute value functions, how do you split them up again? does the negative go in front of the integral or in front of the function inside the integral?

[Anonymous No.2991507]

>>2991357
For part D, implicitly differentiate the original function.
Then manipulate the original function to isolate the Ce^-x part.
Now substitute the value of Ce^-x into the differential equation. You should see that your new equation matches with the old one.

[Anonymous No.2991510]

>>2991505
>>2991505
>>2991505
>>2991505
fuck nvm i realized that the negative inside or outside is irrelevant because they are equivalent

[Anonymous No.2991514]

you guys are just fucking bad

[Anonymous No.2991534]

>>2991505

The fundamental theorem of calculus basically states that integration and differentiation are opposites. When you take a definite integral, you substitute the upper value into the integrated expression and subtract off the lower value. Same thing with variables.

Been a year since I saw calculus, but if all else fails, you can just split up the absolute value function at the places where the function equals 0. Whatever is above the x axis is positive; subtract whatever's below the x axis. Remembering whether to use a subtraction sign or not has always been a pain.

[Anonymous No.2991545]

Take the derivative of both sides

y'' = 1 - y'

Let t = y'

t' = 1 - t

Solve the separable differential equation

-ln(1 - t) = x + C
t = y' = 1 + Ce^-x (absorb a negative into C)

Substitute into the first differential equation and solve for y

1 + Ce^-x = x - y

y = x - 1 + Ce^-x (absorb a negative into C)

[Anonymous No.2991570]

>>2991534
Major fail on my part. But that's a strategy to calculate the integral; just assume there's no absolute value and add the areas "under" the x axis.

[Anonymous No.2991591]

>>2991348

Simply derive the y function with respect to x to get dy/dx set this equal to x-y then put the function given in part d as y and they will equal eachother.

[nancy pelosi invented crack !!sLz+fwCdMOg No.2991623]

so who else took the ap comp sci test today

[Anonymous No.2991651]

>>2991623
i did, thought it was pretty easy compared to most practice tests, although frq #4 was quite tricky