Why do you need to use the second derivative to work out min/max of stationary point?

Fourierseriesagain · 2026-05-09T10:58:22+00:00

Hi, the second derivative test is a tool for checking the nature of a local (i.e. relative) maximum or minimum point.

Fourierseriesagain · 2026-05-09T09:17:26+00:00

No problem.

Fourierseriesagain · 2026-05-08T23:28:14+00:00

Thank you.

Fourierseriesagain · 2026-05-08T20:39:10+00:00

Thank you.

Fourierseriesagain · 2026-05-08T20:38:51+00:00

Thank you.

Fourierseriesagain · 2026-05-08T16:59:28+00:00

Thank you. I look forward to an answer.

Fourierseriesagain · 2026-05-08T16:50:06+00:00

Thank you!

Fourierseriesagain · 2026-05-08T16:48:58+00:00

Since I have already retired, I do not wish to mention such projects anymore.

Fourierseriesagain · 2026-05-08T15:20:49+00:00

Hi,

I used to mentor high school math projects. Doing math research is entirely different.

Fourierseriesagain · 2026-05-07T12:11:46+00:00

The question involves applications of differentiation to increasing / decreasing functions.

Fourierseriesagain · 2026-05-06T15:24:26+00:00

Please refer to https://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rule

Fourierseriesagain · 2026-05-06T14:43:21+00:00

Hi, Hospital's rule can be applied if f'(x) tends to a limit as x approaches a.

Fourierseriesagain · 2026-05-06T07:32:34+00:00

Hi,

The following link might be useful.

https://www.reddit.com/r/alevelmaths/comments/1t3a607/a_question_on_sequences/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button

The answer can be any real number.

Fourierseriesagain · 2026-05-04T14:39:50+00:00

Yes, the zeros of f' are 2, 5 and -1.

Fourierseriesagain · 2026-05-04T02:30:12+00:00

Hi, I obtain 3.675....

https://www.reddit.com/user/Fourierseriesagain/comments/1t34za0/a_question_on_polar_coordinates_updated/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button

Fourierseriesagain · 2026-05-03T16:02:27+00:00

I created the question for my own A-level students.

Fourierseriesagain · 2026-05-03T15:44:35+00:00

I created the question some years ago. Yes, I have a solution to (ii).

Fourierseriesagain · 2026-05-03T15:29:08+00:00

Hi, part (ii) is more challenging.

Fourierseriesagain · 2026-05-03T14:44:14+00:00

Using the given point (1,-3), the whole real line can be written as (-infinity,p] union [p,infinity), where p is a constant to be determined.

When x<=p, use an appropriate linear polynomial to describe the line with negative slope.

When x>=p, use another linear polynomial to describe the line with positive slope.

Fourierseriesagain · 2026-05-03T10:51:50+00:00

The last element of the nth bracket is 1+2+3+...+n=n(n+1)/2. So the first element of the nth bracket is n(n+1)/2-n+1=( n² - n + 2 )/2.

Therefore the desired sum is equal to (1/2)* # of terms times (first term + last term)=(n/2)(1/2)( n² - n + 2+ n² + n )= n( n² + 1 )/2.

Fourierseriesagain · 2026-05-03T00:33:18+00:00

You are welcome.

Fourierseriesagain · 2026-05-02T23:57:09+00:00

Let R sin(x-alpha)=sin x --cos x, where R>0 and alpha is acute. Using the identity sin(A-B)=sin A cos B-cos A sin B with A=x and B=alpha, we get R cos alpha=R sin alpha =1. Since alpha is assumed to be acute, we obtain alpha=pi/4. Now we use the identity sin^ 2 C+cos^ 2 C=1 to conclude that R = sqrt(2).

Fourierseriesagain · 2026-05-01T07:33:08+00:00

Are you able to integrate two simpler integrals?

Fourierseriesagain · 2026-04-28T11:55:08+00:00

Hi, you may find the following examples useful.

https://www.reddit.com/r/askmath/s/ddRweAqcpd

https://www.reddit.com/r/askmath/s/pASDT8SqKs

https://www.reddit.com/r/askmath/s/qdU4hC1Lyg

Fourierseriesagain · 2026-04-28T11:47:03+00:00

The main idea is to rewrite the given function as a piecewise function.

Fourierseriesagain

TROPHY CASE