Determine the exact value of the slope of the tangent line

Thread starter ttpp1124
Start date May 11, 2020
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Line Slope Tangent Tangent line Value

In summary, the slope of the tangent line is a measure of the steepness of a curve at a specific point, and it is calculated using the derivative of the function. It is important to determine the exact value of the slope as it provides valuable information about the behavior of the curve and has various applications in real-world scenarios. The slope can also be negative, indicating a decrease in the function's values or a concave downward curve.

May 11, 2020

ttpp1124

Homework Statement: Can someone check to see if my work is correct? My answer is the slope..

Relevant Equations: n/a

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May 11, 2020

etotheipi

Yep.

Last edited by a moderator: May 12, 2020

What is the slope of a tangent line?

The slope of a tangent line is the rate of change of a curve at a specific point. It represents the steepness of the curve at that point.

How do you determine the slope of a tangent line?

To determine the slope of a tangent line, you need to find the derivative of the curve at the specific point. This can be done using the limit definition of the derivative or through the use of differentiation rules.

Why is it important to determine the slope of a tangent line?

The slope of a tangent line is important because it helps us understand the behavior of a curve at a specific point. It can also be used to find the equation of a tangent line, which is useful in solving optimization problems and finding critical points.

What is the difference between the slope of a tangent line and the slope of a secant line?

The slope of a tangent line is the instantaneous rate of change at a specific point, while the slope of a secant line is the average rate of change between two points on a curve. The slope of a tangent line is a more precise measure of the steepness of the curve at a point.

Can the slope of a tangent line be negative?

Yes, the slope of a tangent line can be negative. This indicates that the curve is decreasing at that point. A positive slope indicates that the curve is increasing at that point.