Close, but why at x=2?fsm said:Take the derivative of the function at 2?
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?fsm said: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?
A unit vector is a vector with a magnitude of 1 and is used to indicate direction. It has no units, hence the name "unit" vector.
To find the unit vector of a given vector, divide each component of the vector by its magnitude. This will result in a vector with the same direction, but a magnitude of 1.
Unit vectors are used to represent direction in a mathematical and physical context. They are also useful in simplifying calculations and equations involving vectors.
In functions, unit vectors are often used to represent the direction of a vector valued function. They can also be used to define a coordinate system, such as the unit vectors i, j, and k in Cartesian coordinates.
No, by definition, a unit vector has a magnitude of 1. Negative magnitudes are not possible for unit vectors.