Math question help! (1 Viewer)

[SanjanaSenthil]

Show that the curve is monotonic increasing for all values of x.
y = x^3 - 3x^2 + 27x - 3


Also, why do people keep saying that the Maths In Focus textbook is really bad? Is there a better textbook?

 

[Aysce]

Show that the curve is monotonic increasing for all values of x.
y = x^3 - 3x^2 + 27x - 3


Also, why do people keep saying that the Maths In Focus textbook is really bad? Is there a better textbook?

y' = 3x^2 - 6x + 27

So lets say x=o, notice how y' = 27 which is greater than 0

Lets take x<0, say x=-6. Plug that into y' and we find that y' = 3(36)-6(-6)+27 = 171 > 0

Test other negative values of x and you'll see that they are all greater than 0 since there is a square, and the negative sign cancels out with the negative sign of -6x.

Doing similarly with x>0, you'll find that it is positive again, hence the curve is monotonic increasing for all values of x

It's not bad but it does not challenge students. Personally, I used it as a starting foundation when learning new concepts and moved on to Cambridge for increased difficulty and past papers.

 

[soloooooo]

Just show it via trial and error a few times.

Maths in Focus is fine.

 

[barbernator]

show that f'(x) is > 0 for all values. To do this show that the discriminant is less than 0 and test a point on the curve to show it must be always positive.

 

[twinklegal19]

When a curve is monotonically increasing you know that its gradient is always positive right? So differentiate the polynomial and you should get a quadratic. To show that the derivative is always positive for all real values of x, either complete the square or show that the discriminant is <0 and the coefficient in front of x^2 is >0(this shows that the quadratic is positive definite, i.e. it is concave up and it always lies above the x axis)

edit: got beaten by barbernator lol

also regarding textbooks, you should seriously consider Cambridge (especially if you do 3U)

 

[SanjanaSenthil]

Okay, thanks everyone!

 

[Aysce]

show that f'(x) is > 0 for all values. To do this show that the discriminant is less than 0 and test a point on the curve to show it must be always positive.

This is a much better method...

 

[SpiralFlex]

Note: Going from left to right.

 

[Sy123]

Just show it via trial and error a few times.

Maths in Focus is fine.

I would give, and so would any right minded teacher give it zero marks.

Maths in Focus is fine for the basics.

 

[SpiralFlex]

Trial an error tests the function in its immediate neighbourhood so it can't be taken as correct.

 

[Capt Rifle]

math in focus is for noobs!

lol naah it doesnt contain much exam style questions. Cambridge is the way to go!