Home school Calculas( high school level)

[Stupid_neko]

Hi.. New at this site, hope I'm posting these stuff on the write place....
well i had these question below for review for an exam, hope someone can help me solve them, i did my solution in Paint program and on paper and am linking where i uploaded them, ( image shack)

-Find the second derivative
1)y=2x^3e^4x
solution
http://img519.imageshack.us/img519/1610/pictureorvideo004sf6.th.jpg (http://img519.imageshack.us/my.php?image=pictureorvideo004sf6.jpg)

2)y=√(x^3+e^-x+5)
** for where 'e^-x' i think the question is wrong,, i think it should be e^x, not sure??
solution
http://img340.imageshack.us/img340/6392/pictureorvideo005fp2.th.jpg (http://img340.imageshack.us/my.php?image=pictureorvideo005fp2.jpg)

3)Find the second derivative of 'y' with respect to "x" where
y=x^2/X^2
solution
http://img340.imageshack.us/img340/6238/pictureorvideo007rt7.th.jpg (http://img340.imageshack.us/my.php?image=pictureorvideo007rt7.jpg)

4)Find the equation of 2 lines, each of slope 5, that are tangent to y=x^3+2X

5) Find the asymptotes for
f(x)=x/√(4x-1)

6)A dragster accelerates down a strip adn then brakes, adn comes to stop. Its position function, s(t) is given by s(t)=3t^2-1/5t^3, s'(t) in meters, 't' in seconds
a) when does the dragster come to a stop
b) how far has the dragster traveled.
Solution
http://img340.imageshack.us/img340/8870/5aso0.th.png (http://img340.imageshack.us/my.php?image=5aso0.png)

7) Find the polynomial with second degree that goes through (1,-1) and whose slope is 1, When x=-1 and where slop is 19, when x=2
solution
http://img457.imageshack.us/img457/3368/pictureorvideo003mp2.th.jpg (http://img457.imageshack.us/my.php?image=pictureorvideo003mp2.jpg)


8) A helicopter takes off from landing pad at 10:48AM and travels south at 150KM/h is planning to land at 10:56AM.
a) how far is the distance between them changing at 10:50AM( to 2 decimal place)
b) Is the distance between them increasing or decreasing at this instant?


I couldn't answer 4,5,8... please help me with them...and check solution
thank you ...

[turdferguson]

For #4, the derivative is a quadratic. There are 2 places where the tan line has a slope of 5. Find the points where it equals 5 (or where that minus 5 equals zero) and then you have 2 points and 2 slopes

[Noober]

8. If he's traveling at 150 km/h, then that's how fast the distance is changing. For b, it depends. If it went past his destination before 10:50, then the distance is increasing, otherwise it's decreasing.

[Stupid_neko]

For #4, the derivative is a quadratic. There are 2 places where the tan line has a slope of 5. Find the points where it equals 5 (or where that minus 5 equals zero) and then you have 2 points and 2 slopes

For quadratic equation i would need a,b and c. but i have only 2 numbers......and how would i find the point where the point equals 5?


Also can anyone check the solutions i did,

thanks

[HallsofIvy]

"For quadratic equation i would need a,b and c. but i have only 2 numbers......and how would i find the point where the point equals 5? "
A "point" can't equal 5! You are looking for the value of x such that the derivative 3x2+ 2= 5. Surely you can solve that equation.

[sstone]

For #1 the final answer(first derivative) is (e^{4x} \cdot 2x^2) \cdot (4x+3) not 2x + 3...you multiplyed by 2 insted 4...

Edit...even more simple it is if you leave it like this 6x^2 e^{4x} + 8x^3 e^{4x} and make a second derivative...

[Stupid_neko]

Edit...even more simple it is if you leave it like this 6x^2 e^{4x} + 8x^3 e^{4x} and make a second derivative...

I factored out the 2x^2, if you factor it back in , you get the same result....So confused,,,dont know where i made mistake sorry sorry,,,,,,,could you show me where i made the mistake,,,

thank you everyone for your help:)

[sstone]

You multiplied it wrongly...
http://shrani.si/thumbs/pictureorv104wr.jpg (http://shrani.si/?pictureorv104wr.jpg)