please! can someone help me with the following problem?

Question

can any one help me to find out the intervals in which
the function is increasing/decreasing
f(x)=(-1/5)x^5-(7/2)x^4
-(40/3)x^3+2

Answer 1

1-just find f'(x)

in this case it will be

-x^4-14x^3-40x^2

2-find the interval of x for the condition f'x>0 for inc and f'x<0 for dec.

here for inc
-x^4-14x^3-40x^2>o
gives x belongs to (-10,-4)u(0,infinity)

for dec
x belongs to (-infinity,-10)u(-4,0)

hopes that this solution will help u

Answer 2

You find an initial root, assume, say (x-2). Divide the above equation by that and you will find the rest of the roots. Find the interval between the roots. It might be discending so you can find the damping constant from it. Choose the initial root in such a way that all the other roots come in as dividends and the assumed one as the divisor.

Answer 3

-infinity to -1 increasing
-1 to +1 decreasing
+1 to infitiy increasing

Answer 4

With the increase in x , f(x) decreases at the interval of (-4561/30)

Answer 5

I don't know.