Find Turning Points & their Nature, using Differentiation

Local maximum & minimum points of a cubic. We start by finding dy/dx to find the stationary points, then find the second derivative to find the nature of the points. Edexcel C2 Jan 2006 Exam Question 7

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[@MathsWithJay]

Wow! Thank you for your lovely feedback Alex.

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[@MathsWithJay]

Thank you Manjula...good luck for your results...in England, students need this for A' level

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[@MathsWithJay]

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[@rahulk4482]

Could you please explain to me why the quadratic equation is being divided by 2 in the beginning. At 3:12

[@MathsWithJay]

It makes it simpler to factorise....but if you choose to use the quadratic formula, you don't need to divide by 2

[@keiraknight3734]

Where did u find these questions and where can I get the mark scheme

[@MathsWithJay]

This came from Edexcel.

[@dylankc1]

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[@utuntupamed6224]

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[@dwaynedsouza7687]

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[@MathsWithJay]

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[@DjFinestWorldWide]

Thank you so so much for the explanation.

[@MathsWithJay]

You're very welcome!

[@joex8au04]

Hi Jay, Thank you so much, but 12x - 10 when x is equal to -1/3, shouldn't answer be -50?

[@joex8au04]

my bad, stupid me!

[@MathsWithJay]

No!

[@zarasaqib1054]

why is there a math error when I used the quadratic formula typed

[@MathsWithJay]

@zara: Where did you type it?

[@junaidzahir7869]

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[@MathsWithJay]

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[@itsaiisha]

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[@MathsWithJay]

Glad it helped!

[@zarasaqib1054]

can we use the b 2 formulae

[@MathsWithJay]

@zara: What are they?

[@margaretmarh]

This helped thank you 😊

[@MathsWithJay]

No problem 😊

[@darkseid856]

But I still didn't understand how differentiating it help us find turning point? I mean how does it works?

[@HaroldWalden]

Differentiating allows you to find the gradient of a function at any point across its domain. One of the fundamental characteristics of turning points is at the moment the function turns around the gradient is zero. So if we can find the x-value of the turning point we can then solve the original function for the y-value. Have a look at this video that I made on the subject: kzbin.info/www/bejne/hILPmpuaiLmGoc0

[@MathsWithJay]

@Harold: Thank you

[@darkseid856]

@@HaroldWalden thank you

[@HaroldWalden]

Maths with Jay no worries 😃 Your videos are great by the way!

[@ramelsasukesampang4881]

Thanks jay! Really Good

[@ramelsasukesampang4881]

Didn't know d²y/dx² before but now I know 👍 👍 👍

[@MathsWithJay]

Glad you liked it!

[@sparklymoon9909]

just saw this and would like to ask about the question that i couldn't solve 😟 can you help me with this question 👉 Determine the stationary points and find their natures for each of the following curves . (a) y = 5 - 2x³ , i got the dy/dx, but i don't know how to do the next step which is, "when dy/dx = 0 " .

[@MathsWithJay]

The next step is to put your dy/dx equal to zero and solve for x, just as in this video.

[@abhinav7715]

what to do if second derivative comes as 0

[@MathsWithJay]

You could look at the sign of the first derivative on each side of the stationary point.

[@xMrHulx]

Do you work at Sparx Maths by any chance ?

[@MathsWithJay]

No...does someone there sound like me?

[@moinuddinkassmi9671]

For part d, why did we require the double differentiation result to find if it was the minima or the maxima. We could just see if the y is higher or lower. Please correct me if I am wrong lol

[@MathsWithJay]

In an exam, you would be expected to do more than just find that the first derivative is zero....there will be some examples where you won't be able to "see" the graph.

[@faaizas2119]

I didn't understand how to find the max and min points using part a. Could you explain please?

[@MathsWithJay]

At what time in the video?

[@faaizas2119]

@@MathsWithJay 9:50 for part d

[@MathsWithJay]

To distinguish between the points, we work out the second derivative...if it is negative, we have a max, and if positive, we know it is a min

[@abidemioluwatoyin2843]

I don't understand hw u got the y =-2/27-5/9+4/3+2

[@ethan-yd6gw]

Is the stationary point the same as a turning point?

[@MathsWithJay]

No: a turning point is a stationary point; however not all stationary points are turning points. At a turning point, there is a local maximum or minimum. Stationary points that are not turning points are horizontal inflection points....for example, look at the graph of y = x^3 at the origin.

[@harrietread1749]

Thank you!!!

[@MathsWithJay]

@Harriet Read: You're welcome!

[@nicktasticartworks]

I'm sorry but I don't get how x is 1/3 at 4:11

[@MathsWithJay]

We solve 3x+1=0 by subtracting 1 from both sides, then divide both sides by 3.

[@nicktasticartworks]

@@MathsWithJay thank you

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[@MathsWithJay]

Thank you!

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Bless you

[@MathsWithJay]

Thank you 😊

[@mohammedsinansaidalavipook3364]

This is the exact question I got

[@MathsWithJay]

Coincidence!

[@betnermhoswa322]

Well explained thanks

[@MathsWithJay]

Glad it was helpful!

[@abelsolomon1339]

how did u find 73 over 27

[@MathsWithJay]

At what time in the video?

[@user-sr3tx2ej8n]

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[@MathsWithJay]

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[@jeevansingh4690]

@@MathsWithJay find how many roots of the equation x^4+2x^2-8x+3 =0 are .(in illustration solution they used graph method but so kindly to you comfort explain by any)

[@bozec5444]

There's a mistake in factorising...the value of x=1and2/3

[@MathsWithJay]

At what time in the video?

[@Khalid-tr4wl]

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[@MathsWithJay]

:)

[@mdaltamaskhan7]

Find dy/dx from x = y log (xy)

[@MathsWithJay]

Are you looking for implicit differentiation?...kzbin.info/www/bejne/Y5LQnKearKekmMU

[@aujbinfaisal]

ily

[@MathsWithJay]

ty

[@abdullahiabdi2491]

U made a mistake during factorization

[@MathsWithJay]

See the last few examples in this video to see how to factorise these quadratics: kzbin.info/www/bejne/qX7NYnp3mJibd7c

[@madalitsosakala998]

I AGREE

[@MathsWithJay]

Great!