Help with an AP Calc AB Problem?

Test Preparation AP Test Preparation
1

<p>Consider the differential equation dy/dx=-2x/y</p>

<p>a) Let y=f(x) be a particular solution to the differential equation with the initial condition f(1)=-1. Write an equation for the line tangent to the graph of f at (1,-1) and use it to approximate f(1.1).</p>

<p>b) Find the particular solution y=f(x) to the given differential equation with the initial condition f(1)=-1.</p>

<p>At first I just separated the variables, took the derivative and came up with the general solution y=sqrt(c-2x^2). Then I solved for C and found it to be 3. But now I realize that is the answer to part b not part a. I'm confused what I even do for part a. How to I find the tangent line?</p>

2

<p>bumpppppppppppppp</p>

3

<p>a) Use slope-intercept form: y-y1=m(x-x1). The point that they gave you is (x1,y1). Find m by plugging in x1 and y1 into dy/dx. Write your equation of the line after plugging in everything (except x and y).</p>

<p>To approximate f(1.1) using the tangent line, just plug in 1.1 for x after you get your equation.</p>

4

<p>Oh wow, that was a lot easier than I thought. I thought I had to separate, integrate, and then find the tangent line.</p>