How do you find the end behavior of # f(x) = 4x- 5x^3#?

1 Answer
Apr 3, 2016

Answer:

Take the derivative, look at the signs.

Explanation:

#f'(x) = 4-15x^2#.
This equation shows the rate of change of #f(x)# at certain x value.
From the equation you can see that #f'(x)>=0# when #-2/sqrt(15)<=x<=2/sqrt(15)#. For all other values, #f'(x)<0#.

The end behavior of #f(x)=4x-5x^3# is that #f(x)# approaches #-oo# as #x -> oo# and #oo# as #x -> oo#.

Note: #f(x)# approaches #oo# as #x# decreases because negative #f'(x)# means #f(x)# decreases as #x# increases.