Calculus - Slope, Concavity, Max, Min, and Inflection Point (3 of 4) 3nd Order Equation

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In this third of four part lecture series I will show you how to find the slope, concavity (concave up/down), max/min, and inflection (horizontal/vertical inflection) point of a third order equation.

[@doodelay]

At first I sort of hated this portion of calculus on part 1 and 2 but once we got to part 3 (this video) I suddenly realized that the answer to my age old question of, "How do they build graphs of functions from scratch without plugging in every value?" was being answered. They first abstract what a function is made of which is a maximum, minimum, x crosses, and inflection points and simply connect the dots from there by plugging away. Brilliant :D

[@km2711]

EXCELLENT...correction at 5:34.... AGAIN, not casting any negativity towards the instructor--he is excellent.

[@Shell1950]

He did it on purpose.

[@WreckingBallers]

Your videos are some of the most helpful calc videos on the internet. Thank you.

[@MichelvanBiezen]

The slope can only change from negative to positive or from positive to negative at a maximum or minimum. Therefore all points between a maximum and a minimum will either have a positive slope or a negative slope.

[@bstlybengali]

-11

[@MichelvanBiezen]

Good catch!

[@marksilao4505]

Thank you sir, for this helpful content that helped those who struggled in math like me.

[@MichelvanBiezen]

Happy to help

[@abidewanggaperwityasmara9303]

Thank you good sir! Clear explanation and very helpful. Best regards from Indonesia.

[@MichelvanBiezen]

Welcome to the channel!

[@YourEmperorStef]

Very good explanation and reasoning as well. Thanks!!!

[@saurabhs4743]

It's really good.. awesome video. thanks a lot:)

[@fahedtariq1716]

Very well explained. Thankyou Sir

[@truongthaiucduong2807]

Very well explained. Thankyou Sir!

[@MichelvanBiezen]

Most welcome!

[@km2711]

Even better--a graphing calculator to confirm the arithmetic.....easily shows that the slope at zero is T ORDINATE (-2,-11)

[@KlaraGadd]

Thank you so much for this video! Helped me so much!

[@CozyCoins]

You are the best ..

[@sulaimanahsan6651]

Thank u Dear sir very helpfulll.....

[@timurmusaev2386]

Awesome, great video!

[@bharathhari6788]

We are both the same sir ! I lost 2 marks in exam because of not multiplying 2 in a derivative 5 mark sum 😅. I hope there is any cure for that

[@MichelvanBiezen]

It is the way our brains are wired. The only solution is to try and slow down, eliminate distractions (I am easily distracted) and complete each step at at time. But then to err is human..... 🙂

[@troybernal5085]

You're the best!!!!!

[@km2711]

I stopped at about 2:35..noticing that f(-2) = NEGATIVE 11, and not +11. When instructing (and Michel is excellent) it nevertheless ALWAYS pays to confirm even the most seemingly trivial arithmetic with a handheld calculator. As we all know, everything in this field is CUMULATIVE----one mistake in the early stages means the final result will be error.

[@firebirdfilms2227]

this guy is so bad at math

[@Dani98664]

Yea, I thought I did it wrong at first until I rechecked on a calculator.

[@saveurself4161]

But HE is a good teacher

[@blissfulsoundsofnature5143]

What if one was given for example, f(x) = 3x^3. Finding both f’(x) as well as f”(x) will equate to 0. How could I find turning points with such a task?

[@MichelvanBiezen]

If both the firs and second derivative = 0 at x = 0 that means there is an inflection point there, and it must be a horizontal inflection point. It also means that there are no local min or max points. (for f(x) = 3x^3 )

[@Golden_Tortoise]

beautiful!

[@MichelvanBiezen]

Thank you!

[@meagharkins]

THANK YOU SO MUCH

[@whitecoat4413]

remarkable

[@joeyborja423]

WOW! Just wow!

[@rabinbk5014]

Sir why have you taken -1 and +1 for concavity?

[@MichelvanBiezen]

When the second derivative at a location of x is negative, the function at that location will be concave down. When the second derivative at a location of x is positive, the function at that location will be concave up.

[@mrinalthakur3946]

sir if the graph is completely concave upward like x^2 then how do we find the maximum .?

[@MichelvanBiezen]

The you find the minimum in the vary same way. Watch the other videos for more examples.

[@shashu1999]

A purely concave upward graph will not have a maximum

[@blip7882]

thank you

[@co8ku]

Great bowtie sir thanks a lot for your help

[@MichelvanBiezen]

Glad it helped

[@estherhozy9475]

Thank u very much

[@Cuyistron]

Hi ;)

[@kabirkrishna8520]

over complicating things that are actually simple...

[@MichelvanBiezen]

We showed the more general approach instead the simplified approach for just this problem.

[@viper619ful]

lol ! u got it wrong ! its actually -11 not 11 ! LMFAO

[@nuzhatsuraiya8367]

he fixed it right away chill