C3 question

Lilly1234567890

How do you do part C of this question?

ImageUploadedByStudent Room1451532488.360206.jpg

Like I sketched the graph for the line y=mx but I still can't seem to get the answer.

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Reply 1

math42

Original post by Lilly1234567890

How do you do part C of this question?

ImageUploadedByStudent Room1451532488.360206.jpg

Like I sketched the graph for the line y=mx but I still can't seem to get the answer.

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The question asks for you to explain it; you don't need a rigorous mathematical proof or anything. Do you have any ideas?

Reply 2

DylanJ42

Original post by Lilly1234567890

How do you do part C of this question?

ImageUploadedByStudent Room1451532488.360206.jpg

Like I sketched the graph for the line y=mx but I still can't seem to get the answer.

Posted from TSR Mobile

Sketch a graph of

y = lnx

and on the same axis sketch the lines

y = \frac{1}{e}x

and

y = 0x

. Now think about where these two lines intersect the curve y=lnx. The answer should be obvious now. :smile:

Reply 3

Lilly1234567890

Original post by DylanJ42

Sketch a graph of

y = lnx

and on the same axis sketch the lines

y = \frac{1}{e}x

and

y = 0x

. Now think about where these two lines intersect the curve y=lnx. The answer should be obvious now. :smile:

ImageUploadedByStudent Room1451567957.914136.jpg

I sketched te curve and this is what I got. I just can't seem to get the answer or maybe I don't understand the ques. Sorry I know this is an easy question !

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Reply 4

math42

Original post by Lilly1234567890

I sketched te curve and this is what I got. I just can't seem to get the answer or maybe I don't understand the ques. Sorry I know this is an easy question !

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Note the gradient of the tangent you are asked to sketch in b and consider this relative to the gradient in part c.

Reply 5

Notnek

Original post by Lilly1234567890

I sketched te curve and this is what I got. I just can't seem to get the answer or maybe I don't understand the ques. Sorry I know this is an easy question !

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Look back at part b : What's the equation of the tangent? Add the tangent to your sketch.

Reply 6

DylanJ42

Original post by Lilly1234567890

I sketched te curve and this is what I got. I just can't seem to get the answer or maybe I don't understand the ques. Sorry I know this is an easy question !

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As the other two have said, the line y=x/e needs reviewing, what is the equation of the tangent in b)?

Don't worry about it :smile:

the "if 0<m<1/e" part probably just looks daunting and it's probably making you imagine the question to be worse than it actually is, once you fix the sketch the question will become very easy :biggrin:

Reply 7

Lilly1234567890

Original post by DylanJ42

As the other two have said, the line y=x/e needs reviewing, what is the equation of the tangent in b)?

Don't worry about it :smile:

Equation of the tangent at B. Is y=x/e right?
How would u draw the sketch for the graph y=x/e. I used the x- y table to end up like that ^^

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Reply 8

Lilly1234567890

Original post by notnek

Look back at part b : What's the equation of the tangent? Add the tangent to your sketch.

Equation of tangent is x/e and I did add it to my graph ^^😞

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Reply 9

Lilly1234567890

Original post by 1 8 13 20 42

Note the gradient of the tangent you are asked to sketch in b and consider this relative to the gradient in part c.

So the gradient in B is 1/e
And the gradient in A is 1/x right?

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Reply 10

math42

Original post by Lilly1234567890

So the gradient in B is 1/e
And the gradient in A is 1/x right?

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Yeah. So you have that the tangent at (e, 1) has gradient 1/e and just graces the curve. Lines with the gradient in part C will be less steep than this line. Imagine rotating the tangent clockwise (while maintaining positive gradient) and you should see why it must cross the curve.
Assuming you've now drawn the tangent on

(edited 8 years ago)

Reply 11

Lilly1234567890

Original post by 1 8 13 20 42

thanks i finally got it !

Reply 12

Lilly1234567890

Sozz but this is actually a continuation to the ques.

ImageUploadedByStudent Room1451657837.376132.jpg

Basically the question part e that I circled

I tried subbing in the x5 value but it doesn't give me a chance of sign to prove that it is a solution

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Reply 13

DylanJ42

Original post by Lilly1234567890

Sozz but this is actually a continuation to the ques.

ImageUploadedByStudent Room1451657837.376132.jpg

Basically the question part e that I circled

I tried subbing in the x5 value but it doesn't give me a chance of sign to prove that it is a solution

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What was your answer to x(small5)? that you worked out in part d

Reply 14

Lilly1234567890

Original post by DylanJ42

What was your answer to x(small5)? that you worked out in part d

So the answer I got was 1.857

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Reply 15

DylanJ42

Original post by Lilly1234567890

So the answer I got was 1.857

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So if x5 is a suitable estimate to the root to three decimal places then, if you were to round

\alpha

to 3dp, it would equal 1.857. Do you agree with this?

Reply 16

Lilly1234567890

Original post by DylanJ42

So if x5 is a suitable estimate to the root to three decimal places then, if you were to round

\alpha

to 3dp, it would equal 1.857. Do you agree with this?

yep, i agree!

Reply 17

DylanJ42

Original post by Lilly1234567890

yep, i agree!

Great

so ignoring all this alpha/x5 stuff for now.

If i asked you to prove to me, using a suitable interval, that to 3 decimal places 1.857 was a root. What two values would you pick?