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

1 Answer
Apr 3, 2016

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.