Equation for the tangent line

[Sophia1787]

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

 

[Dick]

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?

 

[HallsofIvy]

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.

 

[Sophia1787]

so basically 6x^2-5 ?

 

[Sophia1787]

do i then plug in the 2? and solve?

 

[HallsofIvy]

so basically 6x^2-5 ?

"Basically" what about 6x^2- 5?

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?