Finding the Length of AB: Using Point-Slope Form to Solve Calculus Problems

• DeanBH
In summary, the conversation is about a person struggling with calculus problems and asking for help. The expert summarizes the concepts of finding the equation of a line with a given point and slope, and suggests using the point-slope form of the equation. The person expresses their confusion and the expert encourages them to commit the point-slope form to memory.
DeanBH
damn annoying question. I'm basically new to this stuff, simple HS maths to you guys.

f(x) = X/2 -4/x^2 + 1

thats the line.

dy/dx is 1/2 + 8/x^3 that was first question.

2nd = the normal at point (2/1) on the curve above cuts the x and y axes at A and B respectively. Calculate the length of AB leaving answer in simplified surd form.

ok.

gradient of tangent at that point is 1/2 + 8/16 = 3/2

normal is -2/3.

ok, now from here I'm not sure where to go or what to do =( help =)

The gradient is 1/2 + 1.

Now, do you know what the general equation of a line is? And what are the two pieces of information that you have about the required line?

dx said:
The gradient is 1/2 + 1.

Now, do you know what the general equation of a line is? And what are the two pieces of information that you have about the required line?

y = mx + c

y = X/2 -4/x^2 + 1

1 = (3/2)x/2 - 4/x^2 + 1 ?

1 = 3/2 - 4/4 + 1 -wrrroong

I have no idea what I'm doing you see. that's the problem =(

Ok. I'll give you a hint. If you have

1. a point on the line
2. its slope

You'll be able to determine what the line is.

I don't know what to do!

Yes you do.

You know the equation for a straight line, and you know there are three points, one of which is the intersection with the curve (which you have), the other two will pop out when you fit the line to the curve, with the slope you also already have.

... i don't know what to do with the straight line or these points, i don't know where to put the gradient because the line doesn't look like mx + c, i don't know if i have to change some of the X into the number 2 because of the coordinates..i seriously don't know what the hell I am doing.

DeanBH,
the slope-intercept form of a line equation (y = mx + c) is only useful if you already have the y - intercept (the 'c' in the equation). If you have a point that is not the y - intercept, which is frequently the case in calculus problems, then the point - slope form of the line equation is much more handy. Try to find it in your text. It will contain the terms x1 & y1 - substitute the coordinates of the point you know for these.

BTW - because it can be used with any point, the point - slope equation is worth commiting to memory. Even if the point you know is the y - intercept, since x = 0, it reduces to the slope - intercept form.

1. What is the difference between a tangent and a line?

A tangent is a line that touches a curve at only one point, while a line can intersect a curve at multiple points.

2. How are tangents and lines used in geometry?

Tangents and lines are used to describe the relationship between curves and straight lines, and to find the slope and intersection points of these shapes.

3. Can a line be tangent to a curve at more than one point?

No, by definition, a line can only be tangent to a curve at one point.

4. How is the slope of a tangent line calculated?

The slope of a tangent line is calculated by taking the derivative of the curve at the point of tangency.

5. What are some real-life applications of tangents and lines?

Tangents and lines are used in engineering, architecture, and physics to describe and analyze the behavior of curves and straight lines in the natural world.

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