AP Calculus Worksheet: Slope Fields
AP Calculus Worksheet: Slope Fields
AP Calculus Worksheet: Slope Fields
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<strong>Worksheet</strong><strong>Slope</strong><strong>Fields</strong>.nb 1<strong>AP</strong> <strong>Calculus</strong><strong>Worksheet</strong>: <strong>Slope</strong> <strong>Fields</strong>1. Consider the differential equation dy ÅÅÅÅÅÅdx = x4 Hy - 2L.(a) On the axes provided, sketch a slope field for the given differential equation at thetwelve points indicated.y321-1 O1x(b) While the slope field in part (a) is drawn at only twelve points, it is defined at everypoint in the x-y plane. Describe all points in the x-y plane for which the slopes are negative.
<strong>Worksheet</strong><strong>Slope</strong><strong>Fields</strong>.nb 22. Consider the differential equation dy ÅÅÅÅÅÅdx = x2 Hy - 1L.(a) On the axes provided, sketch a slope field for the given differential equation at thetwelve points indicated.y321-1 O1x(b) While the slope field in part (a) is drawn at only twelve points, it is defined at everypoint in the x-y plane. Describe all points in the x-y plane for which the slopes are positive.
<strong>Worksheet</strong><strong>Slope</strong><strong>Fields</strong>.nb 33. Consider the differential equation ÅÅÅÅÅÅdydx = ÅÅÅÅÅÅÅÅÅÅÅ-xy2 . Let y = f(x) be the particular solution2to this differential equation with initial equation f(-1) = 2.(a) On the axes provided, sketch a slope field for the given differential equation at thetwelve points indicated.y21-1 O1 2x(b) Write an equation for the line tangent to the graph of f at x = -1.
<strong>Worksheet</strong><strong>Slope</strong><strong>Fields</strong>.nb 44. Consider the differential equation ÅÅÅÅÅÅdydx = - ÅÅÅÅÅÅÅ2 x(a) On the axes provided, sketch a slope field for the given differential equation at thetwelve points indicated.yy .21-1 O1x-1-2(b) Let y = f(x) be the particular solution to the differential equation with the initialcondition f(1) = -1. Write an equation for the line tangent to the graph of f at (1, -1) anduse it to approximate f(1.1).
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