Derivative and horizontal tangent help

In summary, a derivative is a mathematical concept used to represent the rate of change of a function. It can be found using various methods such as the power rule, product rule, quotient rule, or chain rule. A horizontal tangent line on a curve signifies a point where the slope is equal to zero, indicating that the function is not increasing or decreasing at that point. Finding horizontal tangent lines is important as it can help identify critical points and determine the behavior of a function at a specific point. Additionally, horizontal tangent lines can occur at multiple points on a curve, particularly when a function has a flat portion or a plateau.
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  • #2


Try rewriting the function (8x^2/x^2+8) as (8x^2)(x^2+8)^-1 and then try to take your derivative.
 
  • #3


Or if you do not plan on using chain rule for your derivative, you can keep the function how it is and just use quotient rule.
 

FAQ: Derivative and horizontal tangent help

What is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function. It is the slope of a tangent line at a specific point on a curve.

How do I find the derivative of a function?

To find the derivative of a function, you can use the power rule, product rule, quotient rule, or chain rule. These are different methods of differentiation that allow you to find the derivative of a function based on its original form.

What does a horizontal tangent line represent?

A horizontal tangent line represents a point on a curve where the slope is equal to zero. This means that the function is not increasing or decreasing at that point, and the tangent line is parallel to the x-axis.

Why is it important to find horizontal tangent lines?

Finding horizontal tangent lines can help you identify critical points of a function, such as maximum and minimum values. It can also help you determine the behavior of a function at a specific point.

Can horizontal tangent lines occur at more than one point on a curve?

Yes, horizontal tangent lines can occur at multiple points on a curve. This can happen when a function has a flat portion or a plateau, where the slope is equal to zero at multiple points.

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