Differentiation by rule problem

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Locus

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Dec 3, 2018
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Good morning/ evening. Dad here, helping daughter navigate higher level leaving cert maths book riddled with mistakes.
I am completely lost with this exercise.
It goes as follows:

The tangent drawn to a curve with equation y=3/x at the point (2, 3/2) meets the x axis at A and the y axis at B.
What is the area of the triangle AOB where O is the origin?

I differentiated to -3/xtothepower2 but i dont know what to make of it, nor do i know what to make of the coordinate given, as there are no cutting points nor a straight line i can compute. Please help.
 
Locus said:
Good morning/ evening. Dad here, helping daughter navigate higher level leaving cert maths book riddled with mistakes.
I am completely lost with this exercise.
It goes as follows:

The tangent drawn to a curve with equation y=3/x at the point (2, 3/2) meets the x axis at A and the y axis at B.
What is the area of the triangle AOB where O is the origin?

I differentiated to -3/xtothepower2 but i dont know what to make of it, nor do i know what to make of the coordinate given, as there are no cutting points nor a straight line i can compute. Please help.
Click to expand...
What is the derivative at the given point?

What is the equation of the line through that point with that slope?

What are its intercepts?
 
What you are missing conceptually is that the triangle is formed by the x and y axes and the tangent through the indicated point. Draw a sketch showing A and B. This is the kind of problem where a picture truly is worth a thousand words.

Once you know the tangent line, you have enough straight lines (you only need three).

As for the mechanics, Dr. Peterson has given you the necessary pointers.
 
You have differentiated correctly. At the point (2, 3/2), what is the gradient? (remember that the derivative gives you a "formula" for the gradient at any point.)

Once you have the gradient and a point, do you know how to find the equation of the tangent line?

Can you then find where this line cuts the x-axis and cuts the y-axis?

Now can you find the area of the triangle AOB?

Let us know how you are going and if you are still stuck. :)
 
I thank you all very much. I managed to see where i was going wrong once i woke up the next day. It was just sleep deprivation.
 
Glad all turned out well.

You would have got a quicker answer had you posted this in calculus. I for one seldom look at the forum on differential equations because I know so little on that topic.
 
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