Equation for the tangent line

In summary, to find the equation for the tangent line to the curve f(x) = 2x3 - 5x - 3 at x = 2, you will need to find the derivative of the function and plug in the given value of x to find the slope of the tangent line. Then, use the point-slope form to find the equation of the line, with the given point being the point of tangency. It is important to understand the relationship between derivatives and tangent lines, as well as the equation of a line given a point and slope, in order to solve this problem.
  • #1
Sophia1787
3
0

Homework Statement



Find the equation for the tangent line to the curve f(x) = 2x3 - 5x - 3 at
x = 2



Homework Equations


How do i start this? I'm really confused and have an assignment with a bunch of these questions due tomorrow by midnight... if someone could help me that would be greatly appreciated..



The Attempt at a Solution

 
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  • #2
The derivative f'(x) will give you the slope of the tangent. x and f(x) will give you a point on the curve. If you have a point and a slope, you have the equation for the tangent line, right?
 
  • #3
One of the very first things you should learn in Calculus is that the derivative at a point is the slope of the tangent line. And even before Calculus you should have learned how to write the equation of a line given a point and the slope.
 
  • #4
so basically 6x^2-5 ?
 
  • #5
do i then plug in the 2? and solve?
 
  • #6
Sophia1787 said:
so basically 6x^2-5 ?
"Basically" what about 6x^2- 5?

Sophia1787 said:
do i then plug in the 2? and solve?
Plug 2 into what? Solve what? Please ask complete questions!

I said before that the derivative at a given value of x is the slope of the tangent line at that x. What is the derivative of your function? What is its value at x= 2?

Now, how do you find the equation of a line through a given point with given slope? (And what "given point" does this line go through?
 

FAQ: Equation for the tangent line

What is the equation for the tangent line?

The equation for the tangent line is y = mx + b, where m is the slope of the tangent line and b is the y-intercept.

How do you find the equation for the tangent line?

To find the equation for the tangent line, you need to first find the slope of the tangent line and a point on the line. Then, you can use the point-slope form of a line to write the equation in the form y - y1 = m(x - x1).

What does the slope of the tangent line represent?

The slope of the tangent line represents the rate of change of the function at a specific point. It tells us how much the function is changing at that point.

Can the equation for the tangent line be used to find the derivative of a function?

Yes, the equation for the tangent line can be used to find the derivative of a function. The slope of the tangent line is equal to the derivative of the function at that point.

How is the equation for the tangent line related to the concept of a derivative?

The equation for the tangent line is directly related to the concept of a derivative. The slope of the tangent line is equal to the derivative of the function at that point, which represents the instantaneous rate of change of the function at that point.

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