# Unit vectors and functions

1. 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)

2. Homework Equations
None that I'm aware of.

3. 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?

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Hootenanny
Staff Emeritus
Gold Member
Okay, lets 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?

Take the derivative of the function at 2?

Hootenanny
Staff Emeritus
Gold Member
HallsofIvy
Homework Helper
1. 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)

2. Homework Equations
None that I'm aware of.
How about f '(x0) is the slope of the tangent line to y= f(x) at xb0, two lines are parallel if they have the same slope, and two lines are normal if the product of their slopes is -1?

3. 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?