Yr 12 Maths 1 Help - Get Assistance for Horizontal Tangents & Normals

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In summary, the person is struggling with math problems and needs help with finding horizontal tangents, parallel tangents, and values of a and b in certain equations. They also need clarification on how to find the value of the derivative and the l's in tangent equations.
  • #1
][nstigator
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Im havin some real problems with my maths :( I am behidn coz I went on a holiday for easter. I have a test tomorrow and I really need help :frown:

If anyone could teach me how to do these sort of questions it would be much appreciated.

1. Find all points of contact of horizontal tangents to the curve
y=2√x+1/√x

2. Find equation of tangent to
y=1-3x+12x²-8x³
which is parallel to the tangent at (1,2)

3. The normal to the curve
y=a√x+b/√x
where a and b are constants, has equation 4x+y=22 at the point where x=4. Find the values of a and b.

I haven't had much trouble with other work in the chapter, but I have continously got questions similar to this wrong. Some help would be much appreciated.
 
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  • #2
1. [tex] y'=0 [/tex]

The solve for x.

2. [tex] y'(1) = y' (x) [/tex]

Find x.

3. 4x+y=22, from which k=-4, from which [itex] k_t=1/4 [/itex] From which [itex] y' (4) = 0.25. [/itex]

Edit:

In 2. After you find the point of interest. Find the value of the derivative there, this will equal k (y=kx+l) of the tangent. It is simple then to find l.
 
Last edited:
  • #3
I don't quite understand 2 :(

and where do u get k from?!
 
  • #4
I don't quite understand 2 :(

Edit:eek:ops soz, ment to edit and get rid of the part where I said "where do u get k from"

Edit2: aw crap, I still have no idea for those questions
 
Last edited:
  • #5
The k (y=kx+l) of a tangent of a curve at a certain point is equal to the value of the derivative of the curve at that point. After solving the equation, you will get an x or two that satisfy it. Find the value of the derivative at those points. Find the l's by satisfying that the tangents intersect with the curve at that point.
 

Related to Yr 12 Maths 1 Help - Get Assistance for Horizontal Tangents & Normals

1. What are horizontal tangents and normals in Year 12 Maths 1?

Horizontal tangents and normals are important concepts in calculus. A horizontal tangent is a line that is parallel to the x-axis and touches a curve at only one point. A normal is a line that is perpendicular to the tangent line at a specific point on the curve. In Year 12 Maths 1, these concepts are used to solve problems involving the rate of change and optimization.

2. How do I find the equation of a horizontal tangent line?

To find the equation of a horizontal tangent line, you will need to first find the derivative of the original curve. Then, set the derivative equal to zero and solve for the x-value. This x-value will be the point at which the tangent line is horizontal. Finally, substitute this x-value into the original equation to find the y-value. The equation of the horizontal tangent line will be y = (found y-value).

3. What is the difference between a horizontal tangent and a horizontal line?

A horizontal tangent is a line that touches a curve at only one point, while a horizontal line is a line that runs parallel to the x-axis with a constant y-value. In other words, a horizontal tangent is a type of line that can be found on a curve, while a horizontal line is a type of line that can be found on a graph.

4. How do I find the equation of a normal line?

To find the equation of a normal line, first find the derivative of the original curve. Then, find the derivative at a specific point on the curve. The negative reciprocal of this derivative will give you the slope of the normal line. Next, use the point-slope form of a line to find the equation of the normal line. This equation will be in the form y = mx + b, where m is the slope and b is the y-intercept.

5. Can horizontal tangents and normals be applied to real-life situations?

Yes, horizontal tangents and normals have various real-life applications. For example, they can be used to find the maximum or minimum points of a function, which is useful in optimization problems. They can also be used to calculate the rate of change in a real-life scenario, such as the rate of growth of a population or the rate of decay of a radioactive substance.

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