Horizontal tangent/point of inflection problem

  • Thread starter drandhawa
  • Start date
  • Tags
    Horizontal
In summary, to find the value of b for the function y=x^4+bx^2+8x+1 to have both a horizontal tangent and a point of inflection at the same value of x, you must first find the first and second derivatives, set them equal to 0, and solve for x. Then, substitute the value of x into the first equation to solve for b.
  • #1
drandhawa
9
0

Homework Statement



The function y=x(to the forth)+bx(squared)+8x+1 has a horizontal tangent and a point of inflection for the same value of x. What must be the value of b?

Homework Equations



I think you have to find the derivative, set it equal to 0 and solve for x

The Attempt at a Solution

 
Physics news on Phys.org
  • #2
That's one thing you have to do alright. But the second derivative also has to be zero, doesn't it? I would suggest you solve the equation for the second derivative equal to zero for b and substitute it into the first equation. THEN solve for x.
 

1. What is a horizontal tangent?

A horizontal tangent is a line that is tangent to a curve at a specific point and is parallel to the x-axis. This means that the slope of the curve at that point is equal to 0.

2. How do you find the point of inflection?

The point of inflection is the point where the concavity of a curve changes. To find this point, you can take the second derivative of the function and set it equal to 0. This will give you the x-value of the point of inflection. You can then plug this value into the original function to find the y-value.

3. What is the significance of the horizontal tangent/point of inflection?

The horizontal tangent and point of inflection are important points on a curve that help us understand the behavior of the function. The horizontal tangent can indicate where a function has a maximum or minimum value, while the point of inflection shows where the concavity changes from concave up to concave down or vice versa.

4. Can a curve have more than one horizontal tangent or point of inflection?

Yes, a curve can have multiple horizontal tangents and points of inflection. This can happen if the function has multiple maximum or minimum points, or if the concavity changes multiple times.

5. How can the horizontal tangent/point of inflection problem be applied in real life?

The horizontal tangent and point of inflection are used in many fields, such as physics, engineering, and economics. In physics, the horizontal tangent can represent the point where an object has reached its maximum velocity. In economics, the point of inflection can represent the point where a company's revenue changes from increasing to decreasing. These concepts help us analyze real-world situations and make informed decisions.

Similar threads

Replies
1
Views
440
  • Calculus and Beyond Homework Help
Replies
5
Views
943
  • Calculus and Beyond Homework Help
Replies
4
Views
933
  • Calculus and Beyond Homework Help
Replies
2
Views
221
  • Calculus and Beyond Homework Help
Replies
2
Views
707
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
8
Views
347
Replies
5
Views
1K
  • Calculus and Beyond Homework Help
Replies
19
Views
2K
  • Calculus and Beyond Homework Help
Replies
21
Views
2K
Back
Top