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Unit vectors and functions

  • Thread starter fsm
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fsm
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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?
 

Answers and Replies

Hootenanny
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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?
 
fsm
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Take the derivative of the function at 2?
 
Hootenanny
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HallsofIvy
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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?
 

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