Mathematics Question Thread

[RuiAce]

hi!
how would i do question 14, im so confused!

(Note. We have 1 A0 paper. AND 2 A1 papers. AND 4 A2 papers. And so on. And we're stacking ALL of these papers on top of each other.)

[cxmplete]

Thank you so much

[anotherworld2b]

I'm not sure how to do this question.
Help is appreciated 

[anotherworld2b]

I was also wondering how do you differentiate this function where g is a constant ?

[Shadowxo]

I was also wondering how do you differentiate this function where g is a constant ?

You just need to remember that 2,π and g are all constants so you can just leave them out the front and only worry about the variable.

[Arisa_90]

how do you know that 2 and π are constants?
Does constant simply mean that you do not change them when you differentiate them?
I also wanted to ask what would you do if you were ask to draw f(x) if given f''(x) and vice versa? Would this be a possible question that could be asked?

 

You just need to remember that 2,π and g are all constants so you can just leave them out the front and only worry about the variable.

[Jakeybaby]

how do you know that 2 and π are constants?
Does constant simply mean that you do not change them when you differentiate them?
I also wanted to ask what would you do if you were ask to draw f(x) if given f''(x) and vice versa? Would this be a possible question that could be asked?

Constants are just numbers that stay the same forever (they aren't variable). The number 2 will always be 2, no matter what - this is the same for pi (3.1415....), pi never changes, it's always they same value. Hence, they are constant.

Regarding your graphing question, this is a very common question within the SACE curriculum, not too sure about HSC, but I'd imagine so. With these questions, it is extremely important to understand what f(x), f'(x) and f''(x) represent.

For example: f'(x) represents the rate of change of some quantity (the slope) & f''(x) represents the rate of change of the slope. I find that it is most useful to think about what f'(x) and f''(x) mean when they are equal to 0.

When f'(x) = 0, you have either;

• Maximum point
• Minimum point
• or a Point of Inflection

[Shadowxo]

how do you know that 2 and π are constants?
Does constant simply mean that you do not change them when you differentiate them?
I also wanted to ask what would you do if you were ask to draw f(x) if given f''(x) and vice versa? Would this be a possible question that could be asked?

Constants have values that do not change - their value is constant. 2 is equal to 2, a is equal to a, pi is equal to pi. The value of x can change depending on the x value - x is a variable (changes).
If you differentiate a constant, it equals zero, and the derivative of a constant times a function is equal to the constant times the derivative of the function. eg:
derivative of 2 =0
derivative of 2x³ = derivative of 2(x³) = 2*(3x²) = 6x²

With regards to the graphing, I'm not very familiar with the HSC curriculum but they wouldn't give you f''(x) and just say to graph it. They may ask you to find the points of inflection for a graph, or find f(x) / graph if you're given f''(x) plus when x=1, f'(x)=2 etc (in order to graph it, you'd need coordinates)
Jake does raise some good points though, you should know what each of f(x), f'(x) and f''(x) represent and how to use them.

[anotherworld2b]

How would you do this question?

[Arisa_90]

I get incredibly confused about how to draw a graph from f '(x) to f(x)

Constants are just numbers that stay the same forever (they aren't variable). The number 2 will always be 2, no matter what - this is the same for pi (3.1415....), pi never changes, it's always they same value. Hence, they are constant.

Regarding your graphing question, this is a very common question within the SACE curriculum, not too sure about HSC, but I'd imagine so. With these questions, it is extremely important to understand what f(x), f'(x) and f''(x) represent.

For example: f'(x) represents the rate of change of some quantity (the slope) & f''(x) represents the rate of change of the slope. I find that it is most useful to think about what f'(x) and f''(x) mean when they are equal to 0.

When f'(x) = 0, you have either;

• Maximum point
• Minimum point
• or a Point of Inflection

[jamonwindeyer]

I get incredibly confused about how to draw a graph from f '(x) to f(x)

Why don't you give us an example you are struggling with! We'll work through it for you to show you the process!

[jamonwindeyer]

How would you do this question?

Hey! I'm on my phone so can't do working properly (someone else might tag in),  but the idea is to substitute 1.06L in place of just L (to represent the 6% increase); rearrange the expression to get the regular fraction with a constant out the front - Pull the sqrt(1.06) out the front of the traction. That represents the change in T - Then convert to percentage

[Arisa_90]

Help with these questions please

Why don't you give us an example you are struggling with! We'll work through it for you to show you the process!

[Shadowxo]

Help with these questions please

So for the first, question you know there's a turning point / point of inflection where x=1 and x=2 (dy/dx=0). They also tell us that the graph cuts the x axis at the origin, and no where else. Therefore there's only one x intercept, and it's at (0,0) - this is a point on the graph.
We also know dy/dx<0 between 1 and 2 and no where else, so we know between 1 and 2 the gradient is negative and therefore the graph is going down, and everywhere else it's going up. So the graph starts by going up, passing through (0,0), then starts going down where x=1 - so we know this is a local maximum turning point - then starts going up again where x=2 (before it hits the x axis) - so we know this is a local minimum turning point, then continues going up. Does that help with graphing that?

With the second question, you seem to have the right idea, but remember the graph of f(x) can be as far up and down as you like, so the first one doesn't have to be so far up. For these, just look at the values and how positive/negative they are to see how steep the graph is and use the gradient to get the general shape

How would you do this question?

Jamon's right, just sub in L=1.06L and divide the T values, the constants cancel out and you're left with √(1.06L)/√(L) = √1.06 =  1.03 therefore 3% change

[Arisa_90]

I'm still confused about how to use the gradient.
does it mean that on the f '(x) graph if its below the x axis its negative so the f (x) should be decreasing? how do you know what the gradient is? especially for the third image?

So for the first, question you know there's a turning point / point of inflection where x=1 and x=2 (dy/dx=0). They also tell us that the graph cuts the x axis at the origin, and no where else. Therefore there's only one x intercept, and it's at (0,0) - this is a point on the graph.
We also know dy/dx<0 between 1 and 2 and no where else, so we know between 1 and 2 the gradient is negative and therefore the graph is going down, and everywhere else it's going up. So the graph starts by going up, passing through (0,0), then starts going down where x=1 - so we know this is a local maximum turning point - then starts going up again where x=2 (before it hits the x axis) - so we know this is a local minimum turning point, then continues going up. Does that help with graphing that?

With the second question, you seem to have the right idea, but remember the graph of f(x) can be as far up and down as you like, so the first one doesn't have to be so far up. For these, just look at the values and how positive/negative they are to see how steep the graph is and use the gradient to get the general shape

Jamon's right, just sub in L=1.06L and divide the T values, the constants cancel out and you're left with √(1.06L)/√(L) = √1.06 =  1.03 therefore 3% change