This week in Calculus we took AP tests. I did okay on the first one, but of course horrible at the calculator portion. Go figure. I can honestly say I know most of the stuff, it’s just applying it that gives me trouble. I’m not sure what can help me with this problem but if anyone does know come talk to me!
One thing I know all the steps to but can’t do the actual problem is related rates!
1. Pick out all variables.
2. Pick out all equations.
3. Pick out what you are looking for.
4. Sketch a graph and label.
5. Make an equation with your variables.
6. Take the derivative with respect to time.
7. SUBSTITUTE back into to derivative.
8. SOLVE.
Sounds easy in steps, right? Well I still can’t do the problems. Yay me
I have a feeling limits will be on every AP test so here’s some tips.
Rules for limit of x approaching infinity:
When the top degree is the same as the bottom degree, the limit is the top coefficient over the bottom coefficient.
When the top degree is larger than the bottom degree, the limit is infinity.
When the top degree is smaller than the bottom degree, the limit is zero.
Something I may need help with is tangent lines. I always knew how to do them but now I think I psych myself up and forget how during the test. So this is an easy question someone can help me out with .
Also, I still suck at moving from original to derivative or second derivative and what not. PLEASE HELPPPP!
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okay...
ReplyDeleteif your original is 2x^4
then your derivative would be 8x^3 becasue you take your exponent and multiply it by the coefficent for your new coefficient and then take the exponent they have already given you and subtract one.
then for the second derivative you take the derivative of the first derivative
so you have 8x^3
which means you multiply the exponent by the coeffeient for your new coeffienent giving you 24 and then subtract one from the exponent to get the new one!.therefore you answer is 24x^2!
remember to know the product rule:
if you have 3x[2(x)^2] then you'll have to use this rule:
copy the first and multiply by the derivative of the second, then we will add...the derivative of the first multiplied by the second [original]
therefore..3x(4x)+3[2(x)^2]
simplify: 12(x)^2+6(x)^2 giving you 18(x)^2
you may also have to use the quotient rule:
if you have 2x divided by 3(x)^2 then you will use this rule:
copy the bottom and multiply it by the derivative of the top and subtract the derivative of the bottom multiplied by the top, remember not to put your answer over the bottom squared, so for this one:
3(x)^2[2]-2x(6x) all over [3(x)^2]^2
simplify: 6(x)^2-12(x)^2 over [3(x)^2]^2
giving you -6(x)^2 divided by [3(x)^2]^2
hope this helps
for tangent lines...
ReplyDelete1. Take the derivative of the equation like normal
2. Plug in the x value. This will give you your slope
3. Use the slope you get and the point given and plug into slope intercept form (y-y1)=slope(x-x1)
(If a point is not given and only an x value is given plug the x value into the original which will give you a y value creating a point)
TANGENT LINES
ReplyDelete1. Take the derivative of the equation like normal
2. Plug in the x value. This will give you your slope
3. Use the slope you get and the point given and plug into slope intercept form (y-y1)=slope(x-x1)
You're having trouble with just taking the derivative? Is that what you mean? If so, then I can help you with that in school if you want ^^
ReplyDeletederivatives can get confusing when your switching between graphs..in this you should think, could you have a line graph after the scond derivative..well you could, if you started with a cubic, then a parabola, then a diagnoal line..if you just go down the line of graphs, it kinda comes to you.
ReplyDelete