One of the problems on my AP Calc test:(adsbygoogle = window.adsbygoogle || []).push({});

The point (1,9) lies on the graph of an equation y=f(x) for which dy/dx = 4x*y^(1/2) where x> or = to 0 and y > or = 0

When x=0 y=?

Seperation of variables:

dy/y^(1/2) = 4x dx

Integrate :

2 y^(1/2) = 2x^2 +C now, if you do C now:

2 * (9)^(1/2) = 2 (1)^2 + C

6 = 2 + C

C= 4 ,

plug in 0 for X and 4 for C:

2 y^(1/2) = 2 (0)^2 + 4

y^1/2 = 2

y = 4 when x =0 <--- thats what the answer key said/ teacher marked

What I did:

Seperation of variables:

dy/y^(1/2) = 4x dx

Integrate :

2 y^(1/2) = 2x^2

solve for Y

y^(1/2) = x^2

y = x^4 + C

solve for C

9 = (1)^4 + C

C = 8

y = x^4 + 8

Solve for y(0):

y=8 <--- thats the answer I got, and its a multiple choice question

Since it satisfies the initial condition (1,9) and the derivitive, then 8 is a correct answer, right?

If you take the deriv of where I got y = x^4 from, y^(1/2) = x^2, you still get dy/dx = 4x*y^(1/2), and I merely simplified the equation to put it in terms of Y like it says in the intro: "The point (1,9) lies on the graph of an equation y=f(x)"

Any thoughts? -Thanks

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# Was my test wrong?

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