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[za]

http://www.boredofstudies.org/cours...8_2004_Mathematics_Extension_2_Notes_sbhs.pdf


can som1 plz tell me if hte f '(x) grapgh on the bottom left of page 102 is wrong

 

[turtle_2468]

I reckon it's right...

 

[nit]

The general idea is right...it looks a little wonky and asymmetric, that's all

 

[za]

look at the left side of the origin. the gradient is -ve. doesnt that mean that the graph of f(x) should be decreasing?

 

[mr EaZy]

Za, I think its correct!
The red is the gradient function and the blue is f(x)

On the left hand side the blue function is always decreasing, therefore, the red function is always below zero

 

[mr EaZy]

But take a look at 102, question (f) 2nd last line. Thats a shocker! Does anyone know how to approach that kinda question? ill have to check out the general sin`1 (fn) to be sure

 

[za]

nah mate i think its the other way around. the blue line is f ' (x) and the red f(x)

 

[mr EaZy]

turning back to that question on 102, you were right. It is incorrect as they muddled up the grad fn with f(x). In the next quest, the red and blue are swapped around.

 

[za]

oh k
thnx

 

[mr EaZy]

so u get it? za??

 

[mr EaZy]

look at the question check the red and blue for (a)...

 

[za]

look at the graph.
wen the blue line crosses the x-axis there are turning points on the red one.

 

[mr EaZy]

thats right, it means that the blue is a grad fn.
ok so isee, i was wrong!

thanks that means the next quest is not muddled up

 

[CM_Tutor]

Sorry, but in the graph on page 102, bottom left, the blue is the function f(x) and the red is its derivative f'(x). The y-intercept of the blue is a TP, thus its derivative (red) is zero. As the blue goes to +∞, it flattens, and its gradient goes to zero. Thus, red, f'(x), goes to zero from above. Same for goes for -∞ - f'(x) goes to zero from below.

Now, consider the other interpretation. Red = f(x), Blue = f'(x). At x = 0, Red is increasing, hence it has a positive slope. Its derivative would thus be positive, but blue is negative. Furthermore, as x goes to +∞ red decrease towards zero, and so its derivative is negative and approaching zero from below. This is not what blue is doing.

 

[za]

if only they weere a bit clearer wen setting out hte example.