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?

Question

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) ??

Answer 1

#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.