Another week filled with Ap tests and corrections..
I'm just going to go over some of the problems from those exciting test that I ended up getting wrong.
EXAMPLE 1:
Given f(x)=2x^2-7x-10, find the absolute maximum of f(x) on [-1,3].
*I knew I was suppose to take the derivative and plug in the 7/4. What I didn't know was that you have to plug in your endpoints, too.
f(x)=2x^2-7x-10
4x-7=0
4x=7
x=7/4
2(7/4)^2-7(7/4)-10= -129/8
2(-1)^2-7(-1)-10= -1
2(3)^2-7(3)-10= -13
*You want the absolute maximum so whichever one is the greatest-which is -1.
EXAMPLE 2:
A particle's position is given by s=t^3-6t^2+9t. What is the acceleration at time t=4?
*You are going to use PVA, going from position to acceleration which means taking the derivative twice. Then just simply plut in 4.
t^3-6t^2+9t
3t^2-12t+9
6t-12
6(4)-12= 12
EXAMPLE 3:
The volume generated by revolving about the x-axis the region above the curve y=x^3, below the line y=1, and between x=0 and x=1 is
*This is one on the calculator part, so use your calculator. I got this one wrong because I set up the equations wrong.
(pi) the intergralfrom 0 to 1 (1)^2-(x^3)^2
(enter in calculator!) = 6(pi)/7
What I am getting wrong or don't know?
Can someone explain how to do something like: Find the value(s) of dy/dx of x^2y+y^2=5 at y=1.
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dy/dx implies to take the implicit derivative of the function, but first, I would find x by plugging in y since you will need it to find dy/dx.
ReplyDeletex^2(1) + (1)^2 = 5
x^2 + 1 = 5
x^2= 4
x= + or - 2
The plug or minus here, implies you have to plug in both the plus and the minus when plugging in.
Now take the implicit derivative: x^2 dy/dx + y 2x + 2y dy/dx = 0
dy/dx = -2xy/ x^2 + 2y
Once you have that, simply plug in.
-2(2)(1) / (2)^2 + 2(1)
-4/4+2 = -4/6 = -2/3
Now plug in -2:
-2(-2) (1) / (-2)^2 + (2) (1)
4/4+2 = 4/6 = 2/3
Your answer is + or - 2/3
simply stated, everytime you take the derivative of a y, you place dy/dx after it. then solve for dy/dx in the long run.
ReplyDeleteanytime you see dy/dx.. you're taking the derivative, however after you take the derivative of a y, you must put dy/dx behind it. once you have completed taking the derivative remember to solve for dy/dx. when it's asking for an actuall number answer and gives you a number to begin with.. plug in your original equation then plug in to the actual derivative.
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