Question under differentiation chapter

QueekJJ

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1615721716001.png

I had this question and got lost on where i should start. Also please do not give me answers straight away, just give me like ideas on what steps i should do so i can learn
 

Subhotosh Khan

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View attachment 25713

I had this question and got lost on where i should start. Also please do not give me answers straight away, just give me like ideas on what steps i should do so i can learn
Since you are lost in the beginning - let's start with definition:

What is the definition (mathematical) of the gradient of the curve?

1615726499952.png
 

pka

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View attachment 25713I had this question and got lost on where i should start. Also please do not give me answers straight away, just give me like ideas on what steps i should do so i can learn
Here is a start: \(x^2+7x-9)=(2x+9)(x-1)\).
 

HallsofIvy

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-"The curve \(\displaystyle y= 2x^2+ 7x- 4\) and the line y= 5 meet at the points P and Q."
The first thing you need to do is find the points P and Q: solve \(\displaystyle 2x^2+ 7x- 4= 5\).
That is the same as \(\displaystyle 2x^2+ 7x- 9= 0\) and, as pka points out, \(\displaystyle 2x^2+ 7X- 9= (2x+ 9)(x- 1)\). Once you know P and Q, evaluate the derivative of \(\displaystyle 2x^2+ 7x- 9= 0\) at those points.
 

apple2357

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Alternatively try a picture to see what is going on?
You could sketch y=2x^2+7x−4 and the line y=5.


1615978178049.png

Can you see what the question is asking?
 

QueekJJ

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Ah sorry for the late reply, wasn't able to use my gadget the pass few days... Thanks apple2357 and Hallsoflvy for the help, i now finally understood the question and the steps to answer it.

Just to confirm it, the answer gotten is 11 and -11. Am I correct? :D
 

Subhotosh Khan

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Ah sorry for the late reply, wasn't able to use my gadget the pass few days... Thanks apple2357 and Hallsoflvy for the help, i now finally understood the question and the steps to answer it.

Just to confirm it, the answer gotten is 11 and -11. Am I correct? :D
Answer for what?

You were asked to calculate gradient !

Please share your work.
 

apple2357

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Ah sorry for the late reply, wasn't able to use my gadget the pass few days... Thanks apple2357 and Hallsoflvy for the help, i now finally understood the question and the steps to answer it.

Just to confirm it, the answer gotten is 11 and -11. Am I correct? :D

I can confirm the gradient at the two points of intersection are 11 and -11.
Can you see how the graph suggests a symmetry?
 

QueekJJ

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JeffM

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Your answer is correct, and I suspect your reasoning was correct, but your presentation is hard to follow and outright wrong in one respect.

\(\displaystyle \dfrac{dy}{dx} \text { is NOT equal to } 2x^2 + 7x - 4 \text { because } y = 2x^2 + 7x - 4.\)

What you could have shown is

\(\displaystyle f(x) = y = 2x^2 + 7x - 4.\)

\(\displaystyle y = 5 \implies 2x^2 + 7x - 4 = 5 \implies x = \dfrac{- 7 \pm \sqrt{49 - 4(2)(-9)}}{2 * 2} = \dfrac{-7 \pm {49 + 72}}{4} = 1 \text { or } - 4.5.\)

\(\displaystyle \dfrac{dy}{dx} = 4x + 7 = f’(x).\)

\(\displaystyle f’(1) = 4 * 1 + 7 = 11.\)

\(\displaystyle f’(-4.5) = 4(-4.5) + 7 = - 18 + 7 = - 11. \)

Good work. Correct answers are a whole lot more important than presentation that is sweet and neat.
 

Jomo

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You wrote that 2x^2 + 7x - 4 = 4x+ 7. Do you know what '=' means?
 

QueekJJ

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You wrote that 2x^2 + 7x - 4 = 4x+ 7. Do you know what '=' means?
Yeh i just realized my mistake on doing my working after what JeffM said. Thanks <3
 
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