Find the Horizontal Tangent of f(x)=x^2 + 4x - 1

In summary, to find the horizontal tangent of a function, you need to take the derivative and set it equal to 0. The derivative of a quadratic function can be found using the formula f'(x) = 2x + b. The derivative is necessary to find the horizontal tangent, which represents a point of inflection or a local maximum/minimum on the function. To graph a horizontal tangent, plot the x-coordinate of the point and draw a horizontal line through it.
  • #1
PrudensOptimus
641
0
At what point is the tangent to f(x)=x^2 + 4x - 1 horizontal?

How do you do that? I think it's asking me at what point is x = 0, or undefined, right??
 
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  • #2
Hint:

What is the unique feature about the equation of a horizontal line?
How does that relate to tangent lines?
 
Last edited:
  • #3
Horizontal tangent is where derivative=0, that is x=-2.
 

1. How do I find the horizontal tangent of a function?

To find the horizontal tangent of a function, you need to take the derivative of the function and set it equal to 0. The resulting x-value will be the x-coordinate of the point where the function has a horizontal tangent.

2. What is the formula for finding the derivative of a quadratic function?

The formula for finding the derivative of a quadratic function is f'(x) = 2x + b, where b is the coefficient of the x-term in the original function.

3. Can I find the horizontal tangent without taking the derivative?

No, the derivative is necessary to find the horizontal tangent of a function. The derivative represents the slope of the tangent line at any given point on the function, and setting it equal to 0 allows you to find the point where the tangent line is horizontal.

4. What is the significance of a horizontal tangent in a function?

A horizontal tangent in a function indicates a point of inflection, where the function changes from increasing to decreasing (or vice versa). It can also represent a local maximum or minimum point on the function.

5. How do I graph a horizontal tangent on a function?

To graph a horizontal tangent on a function, you can plot the x-coordinate of the point where the tangent occurs and draw a horizontal line through that point. This line will be tangent to the function at that point.

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