Question: Consider the differential equation dy/dx = e -x . (a) Explain why a solution of the DE must be an increasing function on any interval

Consider the differential equation dy/dx = e-x.

(a) Explain why a solution of the DE must be an increasing function on any interval of the x- axis.

(b) What are

 lim dy/dx and lim dy/dx

 What does this suggest about a solution curve as x †’ ± ˆž

(c) Determine an interval over which a solution curve is concave down and an interval over which the curve is concave up.

(d) Sketch the graph of a solution y = Ï•(x) of the differential equation whose shape is suggested by parts (a) €“ (c).

lim dy/dx and lim dy/dx

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