Using derivatives to determine the increase and decrease of functions

[samuelfarley]

Homework Statement

Given the function, f (x) = 4x^6 - 3x^5

show, using interval notation, where the function is decreasing and increasing.

Please give step-by-step details on using derivatives to analyze functions.

Relevant Equations

f (x) = 4x^6 - 3x^5

many attemps made

 

[PeroK]

What's $f'(x)$?

 

[haruspex]

many attemps made

But to see where you are going wrong or getting stuck we need to see at least one of them.

 

[Delta2]

First step is to find the derivative of the function $f'(x)$. Then to find for which x is $f'(x)=0$, for which x is $f'(x)>0$ and for which x is $f'(x)<0$. Then using the monotonicity theorems that relate the monotony of a function to where the first derivative is positive or negative , you can find for which x the function is increasing and for which x the function is decreasing.