First derivative test:
-take the derivative of the original function
-solve for x (the values will be your critical values)
-set those values up into intervals between negative infinity and infinity
- plug in numbers between the intervals into the function
-this will show you when the function is increasing, decreasing, and you will find max's and mins.
Second derivative test:
-take the derivative of the original function twice
-solve for x values(critical values)
-set up into intervals between infinity and negative infinity
-plug in values between the intervals into the function
-this will show you where the graph is concave up and down, and where there is a point of inflection.
Another concept i have a decent handle on is related rates:
-Write down the given
-figure out which formula they want you to use
-plug in the given
-take the derivative
-solve for the unknown
one thing that i need a lot more help with is intergration. and intergration of trig functions expecially.
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integration is just something that has to hit you, i think.
ReplyDeleteone day it just kinda all made sence in my head..
So, for starters, it the opposite of a derivative..
so integrals of sin is -cos
cos is sin..
and so forth.
Integrate the (the square root of x - 1) ^2/ the square root of x
ReplyDeleteu= the square root of x -1 du = 1/2 x^-1/2
since there is a negative exponent, the x^-1/2 will go to the bottom becoming x^1/2, which is what is needed
but there is an extra 2 at the bottom. To get rid of the 2, you will have to multiply by 2
2 integral u^2
2(1/3) u ^3
2/3 u^3
2/3 (the square root of x -1)^3 +C
integrating is pretty easy unless it gets trickyk w/ functions but is the opposite of a der of x would be 1/2x^2 you had one to the exponent and take the exponent and make a fraction out of it w/ the exponent number as your denominator.
ReplyDeleteThe integral of sin is -cos because the derivative of -cos is sin, and
ReplyDeletethe integral of cos is sin because the derivative of sin is cos
Just remember your derivative formulas for trig integration...Don't get your negatives mixed up!
ReplyDeleteAnd I agree with Steph..it's jut got to click one day =/
integration tips:
ReplyDelete1. Look out for trig identities you can use that will make the integral simpler
2. Substitution! Trig substitution often works
3. Use basic algebraic methods to simplify an expression.