section 2.1: think back to circles in geometry.cf.linnbenton.edu/mathsci/math/maurerv/upload/math251...
Post on 30-Sep-2020
1 Views
Preview:
TRANSCRIPT
Math 251 Section 2.1 2013Monday april 3.notebook April 03, 2017
Section 2.1:
Think back to circles in geometry.
What was a tangent line?
What was a secant line?
In Math 251 we are interested in tangent lines to curves other than circles. What might they look like?
Math 251 Section 2.1 2013Monday april 3.notebook April 03, 2017
What is needed to create the equation of a line?
Keep in mind that a tangent line is just a line. Let's recall how we create line equations.
Math 251 Section 2.1 2013Monday april 3.notebook April 03, 2017We are very interested in the SLOPE of the tangent line to a curve.
The slope of a line gives the rate of change for that linear function.
The slope of the tangent line to a curve gives the rate of change of that function at that point.
EXAMPLE: Find an equation of the tangent line to the curve f(x) = √x at the point (1, 1).
We'll start with a picture.
P Q M PQ
Handout
Math 251 Section 2.1 2013Monday april 3.notebook April 03, 2017
So the slope of the tangent line is the LIMITING VALUE of the slopes of the secant line.
We have the slope of the tangent line at (1, 1) is___________.
The line passes through (1, 1).
Now we can find the equation of the tangent line.
What was your average speed driving in to school this morning?
I live 15 miles from campus.It takes me 20 minutes to get here.
Time (hours)
Distance (miles)
Why are we worried about tangent lines? Why isn't a secant line good enough?
Math 251 Section 2.1 2013Monday april 3.notebook April 03, 2017Average velocity is not always useful information.
Suppose a car hits a tree 50 miles from home after being on the road for 1 hour.
Damage is not determined by average velocity.Damage is determined by the velocity at the INSTANT the car hits the tree.
Time (hours)
Distance (miles) 50
1
Time (hours)
Distance (miles) 50
1
Time (hours)
Distance (miles) 50
1
top related