Finding the coordinates given the tangent and curve

[1141]

Hey I was wondering if anybody could help me out here.

I'm kind of stuck on this question:

Find the coordinates of the point on the curve y = 2x[sup:3sggzway]2[/sup:3sggzway] - 3x + 1 where the tangent has a gradient 1.


I know how to do these equations the other way around, when having to find the tangent when given the coordinates and the curve, but not this way.

Help??

 

[Deleted member 4993]

Hey I was wondering if anybody could help me out here.

I'm kind of stuck on this question:

Find the coordinates of the point on the curve y = 2x[sup:2b2gbx68]2[/sup:2b2gbx68] - 3x + 1 where the tangent has a gradient 1.


I know how to do these equations the other way around, when having to find the tangent when given the coordinates and the curve, but not this way.

Help??

Well - first find the equation that gives tangent-slope of 1. This is the locus of all the points with slope = 1.

Now find the intersection of this locus with the given curve.

There is your point....

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.

 

[BigGlenntheHeavy]

Here is the graph, can you take it from here?

[attachment=0:33npqs87]def.jpg[/attachment:33npqs87]

 

[1141]

Well - first find the equation that gives tangent-slope of 1. This is the locus of all the points with slope = 1.

Now find the intersection of this locus with the given curve.

There is your point....

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.

I looked at the question again, and this is my working out:
First I found the derivative:

f(x) = 2x[sup3uh568w]2[/sup3uh568w]-3x+1
f '(x) = 4x-3

then I found the value of x which would make 4x-3=1:

4x-3=1
4x=1+3
x=1

Then I substituted that value of x into the equation y = 2x[sup3uh568w]2[/sup3uh568w]-3x+1 to find y:

y = 2x[sup3uh568w]2[/sup3uh568w]-3x+1
y = 2(1[sup3uh568w]2[/sup3uh568w])-3(1)+1
y = 0

therefore the point of intersection would be (1,0).
Is that correct??

 

[Deleted member 4993]

Well - first find the equation that gives tangent-slope of 1. This is the locus of all the points with slope = 1.

Now find the intersection of this locus with the given curve.

There is your point....

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.

I looked at the question again, and this is my working out:
First I found the derivative:

f(x) = 2x[sup:2bavshze]2[/sup:2bavshze]-3x+1
f '(x) = 4x-3

then I found the value of x which would make 4x-3=1:

4x-3=1
4x=1+3
x=1

Then I substituted that value of x into the equation y = 2x[sup:2bavshze]2[/sup:2bavshze]-3x+1 to find y:

y = 2x[sup:2bavshze]2[/sup:2bavshze]-3x+1
y = 2(1[sup:2bavshze]2[/sup:2bavshze])-3(1)+1
y = 0

therefore the point of intersection would be (1,0).
Is that correct??

First of all - very good work.

However, you should be able to test your answer by looking at the graph Glenn provided you.

By the way, as far as I can tell - your answers are correct.

 

[1141]

Well - first find the equation that gives tangent-slope of 1. This is the locus of all the points with slope = 1.

Now find the intersection of this locus with the given curve.

There is your point....

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.

I looked at the question again, and this is my working out:
First I found the derivative:

f(x) = 2x[sup:hg9g8jo1]2[/sup:hg9g8jo1]-3x+1
f '(x) = 4x-3

then I found the value of x which would make 4x-3=1:

4x-3=1
4x=1+3
x=1

Then I substituted that value of x into the equation y = 2x[sup:hg9g8jo1]2[/sup:hg9g8jo1]-3x+1 to find y:

y = 2x[sup:hg9g8jo1]2[/sup:hg9g8jo1]-3x+1
y = 2(1[sup:hg9g8jo1]2[/sup:hg9g8jo1])-3(1)+1
y = 0

therefore the point of intersection would be (1,0).
Is that correct??

First of all - very good work.

However, you should be able to test your answer by looking at the graph Glenn provided you.

By the way, as far as I can tell - your answers are correct.

Thanks for the help