Finding the Slope of Secant and Tangent Lines

In summary: Just remember to use the derivative of the parabola to find the slope of the tangent line at point P. In summary, the conversation discusses finding the slope of a secant line, the slope of a tangent line, and the equation of the tangent line at a given point on a parabola. The methods for solving for these values are verified and found to be correct.
  • #1
cvc121
61
1

Homework Statement


The points P (2,-1) and Q (3,-4) lie on the parabola y = -x2+2x-1
a) Find the slope of the secant line PQ.
b) Find the slope of the tangent line to the parabola to the parabola at P.
c) Find the equation of the tangent line at P.

Homework Equations

The Attempt at a Solution


I am just new to calculus and am having trouble determining the slope of a secant and tangent line. My attempt at the questions are attached. Can anyone verify my work to see if I am on the right track? Are my methods for solving for the slopes correct? Thanks! All help is very much appreciated!
 

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  • #2
Yup. Looks good.
 
  • #3
cvc121 said:

Homework Statement


The points P (2,-1) and Q (3,-4) lie on the parabola y = -x2+2x-1
a) Find the slope of the secant line PQ.
b) Find the slope of the tangent line to the parabola to the parabola at P.
c) Find the equation of the tangent line at P.

Homework Equations

The Attempt at a Solution


I am just new to calculus and am having trouble determining the slope of a secant and tangent line. My attempt at the questions are attached. Can anyone verify my work to see if I am on the right track? Are my methods for solving for the slopes correct? Thanks! All help is very much appreciated!
It looks fine.

20160226_203054-1-jpg.96503.jpg
 

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

The slope of a secant line represents the average rate of change between two points on a curve, while the slope of a tangent line represents the instantaneous rate of change at a specific point on the curve.

2. How do you find the slope of a secant line?

To find the slope of a secant line, choose two points on the curve, (x1, y1) and (x2, y2), and use the formula (y2 - y1) / (x2 - x1).

3. How do you find the slope of a tangent line?

To find the slope of a tangent line at a specific point on a curve, you can use the derivative of the function at that point. Alternatively, you can find the average slope of a secant line between two points on either side of the point and then take the limit as those points get closer together.

4. What does a negative slope of a secant or tangent line represent?

A negative slope of a secant or tangent line indicates that the curve is decreasing at that point or between the two points used to calculate the slope.

5. Why is finding the slope of secant and tangent lines important?

Finding the slope of secant and tangent lines is important because it can help us understand the behavior of a curve and make predictions about its future values. It is also a fundamental concept in calculus and is used in many real-world applications, such as calculating rates of change and optimizing functions.

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