Question

let f(x)= 2x^4 - 4x^2 find all c in the interval (-3, 3) such that f'(c)=0 please show all steps!

Answer 1

find f'
f'(x)=8x^3-8x

f'(c)=8c^3-8c

not set f'(c)=0 and solve for c

8c^3-8c=0

Answer 2

\[f'(x)=8x^3-8x=8x(x^2-1)=8x(x-1)(x+1)=0\]This is true when x=0, x=1, x=-1 all of which are in the interval (-3,3)

Answer 3

\[f(x)=2x^4-4x^2=0\]\[\Leftrightarrow f(x)=2x^2(x^2-2)=0\]
\[\Leftrightarrow 2x^2=0 \Leftrightarrow x=0\]

OR
\[x^2-2=0\]\[\Leftrightarrow x^2=2\]\[\Leftrightarrow x = \pm \sqrt{2}\]

Answer 4

it wan't to know when f'=0

Answer 5

he wants*

Answer 6

not f

Answer 7

agreed