Download presentation

Presentation is loading. Please wait.

Published byJohana Fearing Modified over 2 years ago

1
3.1.Tangent Lines and Rates of Change. Average and instantenious velocity. Rita Korsunsky

2
not a tangent, 2 pts of intersection.. c Is it a tangent to the curve at c?. c Is it a tangent to the curve at c? The tangent line to the graph of f is a line that touches the graph at one isolated point and could possibly intersect it again at another point. Tangent Lines Yes! Slope of the graph of f at point c is the slope of the tangent line at point c.

3
Slope Slope of secant line = x y.. Q (x, f(x)) P (c, f(c)) O Let’s first find the Slope of secant line:

4
Finding the slope of the tangent line at pt C Let’s pick 2 nd point closer and closer to C and calculate the slopes of Secant Lines. Watch the animation: Slope of tangent line at pt C Slope of Secant Line when x is approaching to C

5
Slope Slope of tangent line = Let x - c = h x = c + h Slope of tangent line at pt C Slope of Secant Line when x is approaching to C

6
To Find the Equation of the Tangent Line at x=c: 1.Find the slope of tangent at any point x 2. Plug in x = c into m x to find the slope m c at the point (c, f(c)). 3. Substitute coordinates (c,f(c)) and slope m c into the point-slope equation of a line:

7
Example 1 Solution:

8
Average Velocity and rate of change

9
Instantaneous Velocity and rate of change

10
Example 2 A sandbag is dropped from a hot-air balloon that is hovering at a height of 512 feet above the ground. If air resistance is disregarded, then the distance s(t) from the ground to the sand bag after t second is given by: Find the velocity of the sandbag at: (a) t = a sec (b) t = 2 sec (c) the instant it strikes the ground (a) Find Velocity at t = a

11
Example 2 continued (b) Find velocity at t = 2 sec (c) Find velocity at instant it hits the ground

Similar presentations

OK

Blue part is out of 60 Green part is out of 43 Total of 103 points possible Grade is out of 100.

Blue part is out of 60 Green part is out of 43 Total of 103 points possible Grade is out of 100.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on maggi advertisement Constitution day for kids ppt on batteries Ppt on electron spin resonance spectroscopy of organic radicals Ppt on review of related literature in research Ppt on project financing in india Waters view ppt online Download ppt on oxidation and reduction in organic chemistry Ppt on stock market basics Ppt on area of plane figures worksheet Ppt on trade fair circular