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EXAMPLE 3 Sketch the graph of x) = 5xe. (A) The domain of f is R. (B) The x- and y-intercepts are both (C) Symmetry: None. (D) Because both 5x and ex become large as x →oo, we have limx→”5xex=00, As x →-oo, however, ex→ and so we have an indeterminate product that requires the use of lHospitals Rule: 5xlim Video Example Thus the x-axis is a horizontal asymptote (E) f(x) = 5xex + 5e = Since ex is always positive, we see that f(x) > 0 when x + 1 > 0, and f(x) 0 when x + 1 < 0 So fis Increasing onand decreasing on ) and decreasing on (-oo, , , f(-1)- -5e-1 is (F) Because fr-1) a local (and absolute) minimum and f, changes from negative to positive at x =

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