Question

Please help `f(x)=6x^5-10x^3` a. find the `x` coordinates of all max and min points. b. State the intervals where f is increasing?

this is calculus and probably involves the first derivative test

Answer 1

Check below

Explanation:

`f(x)=6x^5-10x^3` , `D_f=RR`

We notice that `f(0)=0`

`f'(x)=30x^4-30x^2=30x^2(x^2-1)`

• `f'(x)>0` `<=>` `30x^2(x^2-1)`

`<=>` `x<-1` or `x>1`

• `f'(x)<0` `<=>` `-1<` `x<1`

Hence, `f` is increasing in `(-oo,-1)` and `(1,+oo)` and decreasing in `(-1,1)`

`f` has global and local minimum at `x=1` and maximum at `x=-1`

Graphical help graph{6x^5-10x^3 [-8.89, 8.9, -4.44, 4.444]}