Unformatted text preview: What is the domain of f(x)? a.
b. For what values of x make f(x) = 0? c. For what values of x is f(x) undeﬁned? d. Determine lim f(x) and lim f(x) x —> 00 x > — 00
e. For every value x = c for which ﬁx) is undeﬁned determine lim f(x) and lim f(x)
x > c+ x > c‘ f. Determine where f(x) is positive and where f(x) is negative.
g. Determine where f ‘(x) is zero and undeﬁned. Also determine where f ‘(x) is positive and where it is negative.
h. Determine where f “(x) is zero and undeﬁned. Also determine where f “(x) is positive and where it is negative. i. For which values of x is f(x) concave up? Concave down? j. Give the x and y coordinates of all inﬂection points? k. For which values of x is the graph of f(x) below the x—axis? For which values is
f(x) above the xaxis? 1. For which values of x is the function increasing? Decreasing? m. Give the x and y coordinates of all relative max’s and relative min’s. Here are the two functions. A. f(x) = 2*x"2/(x"2+2)
f‘(x)==8*x«xA2+2)A2
f‘xx) =—(24*xA2_16y(xA2+2)A3 B. f(x) = (XA2—3)/XA3
f ‘(x) = —(x"2—9)/x"4
f “(x) = (2*x"236)/x"5 c. f(x)= x29 f‘(x) =ﬂx_+_9, f“(x)=__32_
st (x75)2 (x—S)3 D. f(x) = (xl)"(1/5) * (XA2+5*X+6) / (xA2—l6) [Have Maple ﬁnd the derivatives of this
function] 4. Consider the piece of the graph of the function f(x) = 2*x"36*x"212*x+l6 with a domain limited to the closed interval [ O , 5 ].
a. What value of x gives the absolute maximum value of f(x) on this interval? What is the value of the ﬁmction as this x?
b. What value of x gives the absolute minimum value of f(x) on this interval? What is the value of the function as this x? ...
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 Fall '10
 Przybylski
 Calculus

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