something i been having trouble with so ill do a example problem
a bag of flower is dropped off of a roof on to the car, what is the average speed during the first two seconds of falling. Given: y=16t^2 to describe the fall.
x=(0,2)- this represents the first two secons.
to find your y's you would plug the first x and then the second x into the given equation.
f(0)=0 and f(2)=16(4)=64
after completin those steps, you plug in to your slope formula.
(y2-y1)/(x2-x1)=(64-0)/(2-0)= 32
the average speed of this particular problem would be 32 m/s.
x=(0,2)- this represents the first two secons.
to find your y's you would plug the first x and then the second x into the given equation.
f(0)=0 and f(2)=16(4)=64
after completin those steps, you plug in to your slope formula.
(y2-y1)/(x2-x1)=(64-0)/(2-0)= 32
the average speed of this particular problem would be 32 m/s.
FIRST DERIVATIVE TEST STEPS AND EXAMPLE
1. take the deriv.
2. set the deriv. equal to zero.
3. solve for the xmax, mins, horizontal tangents and the critical points, (if you don't know how to do this i'll explain in a second.)
4. set up intervals using the step above.
5. plug in to the first deriv. (which is why it's called the 1st deriv. test)
6. plug in values from above to the original function to find the absolute max and min, but only do this if it asks for it.
EXAMPLE:
x^2-6x+8
2x-6
2x-6=0
x=3 is the critical point.
the intervals are (-infinity, 3)u(3,infinity)
.. after you set up the intervals, plug in numbers within the intervals to see whether or not the intervals are increasing or decreasing and if they are a max or min. so in this case you could plug in 2 and 4.
2. set the deriv. equal to zero.
3. solve for the xmax, mins, horizontal tangents and the critical points, (if you don't know how to do this i'll explain in a second.)
4. set up intervals using the step above.
5. plug in to the first deriv. (which is why it's called the 1st deriv. test)
6. plug in values from above to the original function to find the absolute max and min, but only do this if it asks for it.
EXAMPLE:
x^2-6x+8
2x-6
2x-6=0
x=3 is the critical point.
the intervals are (-infinity, 3)u(3,infinity)
.. after you set up the intervals, plug in numbers within the intervals to see whether or not the intervals are increasing or decreasing and if they are a max or min. so in this case you could plug in 2 and 4.
And i still really need help with integrating
its just getting harder
LE2010 said...
ReplyDeleteso integration is.. simple..i guess
if you have to integrate 2x^1/2
then add one to the exponent: 2x^3/2
multiply the coefficent by the reciprical of the new exponent: 3x^3-2
so that's your integral
as for anything else, these are simple terms...
you can look at like the integral of [sin(x)]^2
it would be 1/3[sin(x)]^3 TIMES -cos(x)
you have to times it by -cos because the derivative of -cos is sin..therefore the integral of sin is -cos
HOPE THIS HELPS!