Решите неравенство f'(x)⩽0 f(x) f(x)= 1/4x^4 - 1/3x^3 - x^2

Question

Решите неравенство f'(x)⩽0 f(x)
f(x)= 1/4x^4 - 1/3x^3 - x^2

Answer 1

F'(x)=( 1/4x^4 - 1/3x^3 - x^2)'=1/4*4x³-1/3*3x²-2x=x³-x²-2x
f'(x)=x³-x²-2x
x(x²-x-2)≤0
D=1+8=9=3²
x₁=(1+3)/2=2
x₂=(1-3)/2=-1
x(x+1)(x-2)≤0
x∈(-∞; 0]∨[-1; 2]