math Find slope and concavity of the graph of x2y + y4 = 4+ 2x at (-1,1). Consid
ID: 2848405 • Letter: M
Question
math
Find slope and concavity of the graph of x2y + y4 = 4+ 2x at (-1,1). Consider y = Ax3 + 6x2 - Bx, where A and B are constants. Determine A and B, if it is possible, so that the graph of y has a maximum value at x = -1 and an inflection point at x = 1. Suppose that the amount of money in a bank account after x years is given by Determine the minimum and maximum amount of money in the account, during the first 10 years. The first, year is considered as 0, that is, consider S(x) on [0,10]. Justify your answer.Explanation / Answer
1.
2xy +x^2y' +4y^3 y' = 2
=>
-2 +5y' = 2
=> y' = -4/5
2xy'+2y +2xy' + x^2y" +12y^2y' +4y^3y" = 0
=>
8/5 +2 +8/5 +y" -48/5 +4y" = 0
=>
5y" = 22/5
=> concave upwards
2.
y' = 3Ax^2 +12x -B
y" = 6Ax +12
=>
6A +12 = 0
=>
A = -2
3A -12 -B = 0
=>
B = -18
3.
S' = -10[e^(5-x^2 /8) ](1-x^2/4) = 0
=>
x = 2, -2
S(0) = 2000
S(2) = 199.66
S(10) = 2000 - 100e^(-7.5) = 1999.94
=>
maximum amount = 1999.94
minimum amount = 2000 -20*e ^4.5 = 199.66
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