The discussion revolves around finding unit vectors that are parallel and normal to the graph of the function f(x) = x² at the point (3, 9). Participants are exploring the mathematical concepts related to tangent lines and slopes in the context of calculus.
The discussion is ongoing, with participants attempting to clarify the process of finding the tangent line and its slope. Some guidance has been offered regarding the relationship between slopes of parallel and normal lines, but there is no explicit consensus on the next steps.
Participants express a lack of familiarity with the concepts involved, indicating that this type of problem has been challenging for them in the past. There are no specific equations or methods provided, and the discussion reflects a need for foundational understanding.
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?