How Do You Find Unit Vectors Parallel and Normal to a Curve at a Specific Point?

[fsm]

Homework Statement

Find a unit vector that is (a) parallel to and (b) normal to the graph of f(x) at the given point. Then sketch.

f(x)=x^2
point=(3, 9)

Homework Equations

None that I'm aware of.

The Attempt at a Solution

Find parallel or perpendicular lines, planes, vectors, etc. to a given function has always been a problem for me. I never know where to start. Is it a matter of slope? If so, then how?

 

[Hootenanny]

Okay, let's start with (a); first we must find an equation for a line parallel to the function at this point, that is the equation of the tangent at this point. How do you suppose we can do this?

 

[fsm]

Take the derivative of the function at 2?

 

[Hootenanny]

Take the derivative of the function at 2?

Close, but why at x=2?

 

[HallsofIvy]

Homework Statement

Find a unit vector that is (a) parallel to and (b) normal to the graph of f(x) at the given point. Then sketch.

f(x)=x^2
point=(3, 9)

Homework Equations

None that I'm aware of.

How about f '(x₀) is the slope of the tangent line to y= f(x) at x^b0, two lines are parallel if they have the same slope, and two lines are normal if the product of their slopes is -1?

The Attempt at a Solution

Find parallel or perpendicular lines, planes, vectors, etc. to a given function has always been a problem for me. I never know where to start. Is it a matter of slope? If so, then how?