Dekoyl's question thread

[Mao]

point of inflection [non stationary] is not part of the Methods course


however, I will solve it nevertheless:

point of inflection is a point where the curvature changes. [think about the yin-yang picture, the centre of that is where the curvature changes]
this occurs when the second derivative is 0. the point of inflection can also be stationary, this is called a stationary point of inflection. [think ]

for this case:





this occurs at on the interval , hence solving ,

subbing into original, ,

[Collin Li]

point of inflection is a point where the curvature changes. [think about the yin-yang picture, the centre of that is where the curvature changes]
this occurs when the second derivative is 0.

To be more precise, this is when the second derivative changes sign (so if the second derivative is 0, and merely "touches" the x-axis, it will not suffice). This is because when the first derivative reaches a local maxima or minima, there is a change in curvature. Hence, a turning point in the derivative (i.e.: when the second derivative is zero), is a change in curvature - an inflection point.

[dekoyl]

@Mao: The Yin-Yang example was nice.
You didn't need to find the tangent equation as well but your efforts are appreciated.
Many thanks.

@Coblin Cheers for the extra clarification

[humph]

point of inflection in this case = point where second derivative is zero.

As the second derivative of cosine is negative cosine, the points of inflection will just be the zeroes of cosine. In your case above, , and so the point of inflection is .

[dekoyl]

mao why did u use double derivatives in a methods question? that's just rude.

LOL.

Thanks humph.

[dekoyl]

I'm having a tiny bit of trouble finding the variables (not sure if it's the right term to use) in this question.

1. Use Euler's method of linear approximation to find the value of Leave the approximation in exact form.

Might save you a little time:





2. When dealing with modulus functions, are there cases where the inequality doesn't seem to make sense? (I just came across one.) For example, you cant keep the inequality sign in place when solving quadratics.
Eg:

            is wrong.
So in other words, I'd have to visualize the graph to make sense?

Thank you.

[Mao]

1. this question is terribly worded, so I'm going to go with my interpretation:











2. yes, visualisation is always the best way to go.

[dekoyl]

Thanks Mao that's what the answer wanted.

VN was a bit quiet today

[dekoyl]

Very easy question:

The gradient of the tangent to the curve at equals?

I keep getting 23.42 (2 d.p.) but the answers says 2.373. Is my calculator faulty?
There was also a case in a practice exam where all my y-coordinates for a graph were wrong (and I'm pretty sure I entered the equation correctly.)
Just checking with you guys.

Thanks.

[shinny]

I'm getting 2.373 on my CAS, so their answer is definitely correct. I doubt your calculator is faulty, rather, its probably a case of typoing despite you thinking you haven't. Reason why I suspect this is because I actually typo'd it twice myself just then even with the intention of not doing so, so check through once more I guess, counting the number of brackets you use.

[dekoyl]

Hmm.. still not getting it on my Ti-84.

This is what I put in(exactly so I'm not going to use LaTex):

=(X/2)(tan(√(Xe^(X)))

[Collin Li]

X/2 will read as .

Be careful about that. Use brackets

[dekoyl]

X/2 will read as .

Be careful about that. Use brackets

Ahh. Can't believe I didn't see that.
Thanks again, Coblin.

Question solved.

[shinny]

Yep, that was the second error I had =P Told ya.

[dekoyl]

Hello once again. I have a mental block. Could someone help me unblock this block?
How does:



simplify to:



Thank you.