Home school Calculas( high school level)

by Stupid_neko
Tags: calculas, home, school
 P: 3 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 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 3)Find the second derivative of 'y' with respect to "x" where y=x^2/X^2 solution 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 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 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 ...
 P: 312 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
 P: 20 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.
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Home school Calculas( high school level)

 Quote by 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
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
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,552 "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.
 P: 14 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...
P: 3
 Quote by sstone 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:)
 P: 14 You multiplied it wrongly...

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