How do I find the slope of the tangent line for a given x-coordinate?

In summary, the conversation discusses finding the slope of the tangent lines to a parabola with the equation y=x^2+4x-1 and a given x-coordinate of -3. The speaker is seeking help with this problem and questions if the other person has knowledge of calculus and derivatives.
  • #1
thats.life
2
0
Hello there. I am kind of confused about this and have no idea where to start.
FOr example:

If the line given is y=x^2+4x-1 and we are to find the slope of the tangent of the perpendicular line which passes through x-coordinate -3.


Where do I start?
 
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  • #2
Figure out what point (-3, ?) you are discussing. Then, do you know how to find the slope of a curve at a point? And do you know the relation between the slopes of two lines which are perpendicular to each other?
 
  • #3
Ohh I am sorry. Disregard the perpendicular part.
So what I am asking is:

How do i find the sloper of the tangent lines to the parabola y= x^2 + 4x -1 if I am only given the x-coordinate -3. That is all the information stated.

I need help from step one. I have no idea how to even approach this.
 
  • #4
thats.life said:
Ohh I am sorry. Disregard the perpendicular part.
So what I am asking is:

How do i find the sloper of the tangent lines to the parabola y= x^2 + 4x -1 if I am only given the x-coordinate -3. That is all the information stated.

I need help from step one. I have no idea how to even approach this.

Well, surely you can figure out the y value for x = -3.

Are you taking a calculus course? Do you know about derivatives and their relation to slope?
 

FAQ: How do I find the slope of the tangent line for a given x-coordinate?

What are limits and rates of change?

Limits and rates of change are concepts in calculus that describe the behavior of a function as it approaches a certain value or changes over time. Limits refer to the value that a function approaches as its input variable gets closer and closer to a specific value. Rates of change, also known as derivatives, describe the instantaneous rate of change of a function at a specific point.

How do you find the limit of a function?

To find the limit of a function, you can use algebraic techniques such as factoring, simplifying, and rationalizing the denominator. You can also use graphical methods by plotting the function and observing its behavior as the input variable approaches the desired value. Additionally, you can use calculus techniques such as L'Hopital's rule or the squeeze theorem to evaluate limits.

What is the difference between a one-sided limit and a two-sided limit?

A one-sided limit only considers the behavior of a function as the input variable approaches a specific value from one direction, either the left or the right. A two-sided limit, on the other hand, takes into account the behavior of the function from both the left and the right as the input variable approaches the desired value. In other words, a two-sided limit provides a more complete understanding of the behavior of a function at a specific point.

How are limits and continuity related?

Limits and continuity are closely related concepts in calculus. A function is considered continuous at a point if its limit exists at that point and is equal to the value of the function at that point. In other words, for a function to be continuous, its limit and its value at a specific point must match. If this condition is not met, the function is considered discontinuous at that point.

What are the applications of rates of change in real-life situations?

Rates of change, or derivatives, have many applications in real-life situations. They can be used to describe the speed and acceleration of moving objects, the growth and decay of populations, and the change in value of financial investments. They also have applications in fields such as physics, economics, and engineering, where understanding the rate of change is crucial in solving problems and making predictions.

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