AP CALC. AB
posted by Darcy .
2. A cubic function is a polynomial of degree 3 and has the form y=mx^3+bx^2+cx+d; m≠0. What is the maximum quantity of local extreme values a given cubic function can have?
a. 2
b. 1
c. 0
d. 3
Is it (a)??
2. Let f(x)=xln(x). The minimum value attained by f is
a) there is no minimum
b)1/e
c)1/e
d)1
e)0
is it (a) ??

#2 (a) is correct
#3 f' = lnx + 1
The only extremum is at x = 1/e
f" = 1/x, which is positive at 1/e, so f(1/e) is a minimum.
Looks like (c) is the answer
See the graph at
http://www.wolframalpha.com/input/?i=x*lnx
Ignore tha part where x<0, since lnx is not real there.
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