Use test to show that the function is odd, even, or neither. Find where f'(x)=0. Just solve, no need to label anything else. f(x)=(4/5) x^5 - (2/3) x^3 - 2x

Answer 1

If f(-x) =-f(x) then odd

if f(-x) = f(x) then even

f(-x) = -(4/5)x⁵+(2/3)x³+2x = -f(x) Since -1 to odd power is still -1, So odd function

f'(x) = 4x⁴-2x²-2

-2 factors are ±1,2

f'(1) = 0

f(-1) =0

dividing f(x) by (x+1) and (x-1) leaves

4x²+2

The other zeroes are complex.

x = 1,-1