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Math · Calculus
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Name:S Consider the differential equation 2x-y. (a) On the axes provided, sketch a slope field for the given differential equation at the six points indicated. -1 (b) Find d in terms of x and y. Determine the concavity of all solution curves for the given differental dx2 equation in Quadrant II. Give a reason for your answer. (c) Let y - f(x) be the particular solution to the differential equation with the initial condition f(2) 3. (d) Find the values of the constants m and b for which y mx+ b is a solution to the differential eq Does / have a relative minimum, a relative maximum, or neither at x 2? Justify your answer.
Graph of f 3. The function f is defined on the closed interval [-5, 4]. The graph of f consists of three line segments and is shown in the figure above. Let g be the function defined by a6-)ro (a) Find g(3). (b) On what open intervals contained in -5 < x <4 is the graph of g both increasing and concave down? Give a reason for your answer. e) The function lh is defined by h)- se). Find Ih(3). 5x (d) The function P is defined by p(x)-f(x2-x). Find the slope of the line tangent to the graph of p at the point wherex--1.
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