Question

let f(x)=ax^3 + bx^2 + cx + d, a=0
a. show that f has either 0 or 2 local extrema
b. give an example of each possibility in part (a)

Answer 1

a=0?

Answer 2

or a cannot equal zero?

Answer 3

if a=0 you get

f'(x)=2bx+c

Answer 4

0=2bx+c

c=-2bx

Answer 5

x=c/-2b

Answer 6

if a>0 then you get a quadratic polynomial in which you get 2 answers

Answer 7

a equal to 0.

Thanks... so how does this prove that f has 0 or 2 extrema..?