Showing increasing functions

[last parcel]

Any help is greatly appreciated

[final shell]

increasing means f'(x)>=0

so differentiate and u get 5x^4 - 30x^2 + 50

are you stuck there?

[last parcel]

No I just didnt think of that

What would you do from there?

solve?

[final shell]

no

you have to prove that that is always >=0

[last parcel]

How would u do that?

[final shell]

have a go first

[last parcel]

Alright

thanks brother

Diff of 2 squares?

[final shell]

how will that prove its bigger or equal to 0

[last parcel]

discriminant

its below 0 I did it

But then you know the final point

thats where I struggle

Like that shows there are no real roots

so no x values

So then from there idrk how to say its always an increasing function

[final shell]

ok thats one way

since its a positive x^4 graph then if there are no real roots it must be above the x-axis for all x thus 5x^4 - 30x^2 + 50 will never give a negative output

so >=0

or what you could do is complete the square

[last parcel]

Oh I see

like say y=x^2

[final shell]

yep

[last parcel]

Thanks so much man