F(X)=x^4+3x^3-x^2-8x+2

Question

i need to know where the function is increasing or decreasing 

Answer 1

Use F'(x) to tell where F is increasing/decreasing.

 

F'(x) = 4x³ +9x² -2x -8; it has one rational zero at -2 so F'(x) = (x+2)(4x²+x-4) and that quadratic factor has its zeros at {-1.1228,0.8828}

 

Graph F' (the cubic function) and observe that it's negative on (-infinity,-2) and (-1.1328,0.8828) ⇐ so F is increasing

and F' is positive on (-2,-1.1328) and (0.8828,infinity) ⇐ so F is decreasing