[kathryn25t]

Really struggling with these questions, i understand the method of differentiating ln and how to answer the questions, i just keep getting a different answer to the answers in the book! just wondered if someone could maybe help me figure out where i'm going wrong?

1. Find any stationary values of the following curve and determine whether they are maxima or minima -
y = – ln2x

When i differentiate this is i get x -

Then set dy/dx to 0, getting 0 = x -
So x = 1 or -1?
But the answer given in the book is x = - ln2?

Also the other question i'm having problems with is:

Find the equation of the normal at x=2 to the curve with equation y = ln(2x-3).

The answer that i'm getting is y = x - 1, but apparently this is also wrong.

The book i'm working from is cambridge advanced mathematics core 3 & 4 for ocr

If anyone could help i would be so grateful, been trying to figure these questions out for ages now and getting so frustrated!

[insparato]

For the first question, your working is right but remember setting dy/dx = 0 is finding the x coordinate of the stationary value. You have to put x = 1/-1 BACK into y to get your y coordinate for the stationary point. Also remember the question is asking which ones are maxima and minima which you need to do some more working out for that.

For the second question some working out would be helpful to see where you're going wrong.

[raheem94]

(Original post by kathryn25t)
Really struggling with these questions, i understand the method of differentiating ln and how to answer the questions, i just keep getting a different answer to the answers in the book! just wondered if someone could maybe help me figure out where i'm going wrong?

1. Find any stationary values of the following curve and determine whether they are maxima or minima -
y = – ln2x

When i differentiate this is i get x -

Then set dy/dx to 0, getting 0 = x -
So x = 1 or -1?
But the answer given in the book is x = - ln2?

is not a solution because it will make the natural log negative.

Substituting in gives so the answer you are reading is the y-coordinate.

[raheem94]

(Original post by kathryn25t)

Also the other question i'm having problems with is:

Find the equation of the normal at x=2 to the curve with equation y = ln(2x-3).

The answer that i'm getting is y = x - 1, but apparently this is also wrong.

The book i'm working from is cambridge advanced mathematics core 3 & 4 for ocr

If anyone could help i would be so grateful, been trying to figure these questions out for ages now and getting so frustrated!

I get the answer as

What is the answer in the book?

[kathryn25t]

(Original post by insparato)
For the second question some working out would be helpful to see where you're going wrong.

My working is this:
dy/dx =

Therefore the gradient of the normal will be

When x=2, the gradient of the normal is 1/2 and the y co-ordinate will be ln1 = 0.

So the final equation of the normal i got to be

and the answer given in the book is y = 1-
so my answer is nearly correct, i'm must be going wrong with the signs somewhere but i cant seem to see where i'm going wrong,
i'm probably just making a really silly mistake and being totally blind but if anyone could point this out i'd be grateful?

[aznkid66]

Gradient of normal is negative reciprocal, not reciprocal.

[kathryn25t]

(Original post by aznkid66)
Gradient of normal is negative reciprocal, not reciprocal.

ah yes, that would be the problem!

thank you so much for all of your help!