Heyyyyyyyyyyy! Happy Valentines Day. Well I'm hyper, and I just remembered about my blog. So here we goooo...
REMEMBERING:
POSITION
VELOCITY
ACCELERATION
If going down (like position to velocity, or velocity to acceleration) take derivative. If going up (going from acceleration to velocity) take integral. Real simple!
FINALLY I UNDERSTAND THIS SIMPLE THING:
It's called the chain rule. Take derivative of exponent, the derivative of the like sin, cos, tan, ect., then the derivative of inside & remember to simplify.
Example:
sin^2(x^2)
4xsin(x^2)cos(x^2)
RELATED RATES:
1. identify all variables and equations
2. identify what you are looking for
3. sketch and label
4. write an equations involving your variables (you can only have one unknown so a secondary equation may be given)
5. take the derivative (with respect to time)
6. substitute in derivative and solve
EXAMPLE:
The variables x and y are differentiable functions of t and are related by the equation y=2x^3-x+4. When x=2, dx/dt=-1. Find dy/dt when x=2.
1. All of your equations are given, go straight to derivative.
2. dy/dt=6x^2dx/dt-dx/dt
3. plug in all your given (in order) to find dy/dt
dy/dt=6(2)^2(-1)-(-1)dy/dt= -23
YOU COULD PROBABLY COMMENT ON:
So I don't have all my ap stuff with me, and I don't remember an exact problem I'm having trouble with. Can someone tell me about mean value theorem again? And for some reason I'm still having trouble with piecewise function things, no matter how many times it is explained. Can someone put it in any simpler terms or something?
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the mean value theorem states, roughly, that given a section of a continuous (differentiable) curve, there is at least one point on that section at which the derivative (or slope) of the curve is equal (or parallel) to the "average" derivative of the section.
ReplyDeleteso to do these, basically you are finding a value of c such that f'(c) = f(b)-f(a) / b-a.
something i grabbed off the internet to help you understand this a bit better:
This theorem can be understood intuitively by applying it to motion: If a car travels one hundred miles in one hour, then its average speed during that time was 100 miles per hour. To get at that average speed, the car either has to go at a constant 100 miles per hour during that whole time, or, if it goes slower at one moment, it has to go faster at another moment as well (and vice versa), in order to still end up with an average of 100 miles per hour. Therefore, the Mean Value Theorem tells us that at some point during the journey, the car must have been traveling at exactly 100 miles per hour; that is, it was traveling at its average speed.