Attempted this but stuck on the missing boxes. EXAMPLE 3 Sketch the graph of f(x
ID: 2840313 • Letter: A
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Attempted this but stuck on the missing boxes.
EXAMPLE 3 Sketch the graph of f(x) = 4xe x. The domain of f is R. The x- and y-intercepts are both . Symmetry: None. Because both 4x and ex become large as x rightarrow infinity, we have limx rightarrow infinity4xe x = infinity. As x rightarrow -infinity, however, ex rightarrow and so we have an indeterminate product that requires the use of I'Hospital,s Rule: Thus the x-axis is a horizontal asymptote. f'(x) = 4xe x + 4e x = Since ex is always positive, we see that f'(x) > 0 when x + 1 > 0, and f'(x) and f"(x)Explanation / Answer
D) -e^(-x)
E) 4(e^x)(x+1)
G) the 6 blanks in (G) are 4(e^x)(x+2) , -2 ,-2, (-infinity,-2) ,(-2,infinity), (-2,-8*e^-2) in order!
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