Download presentation

Published byColin Bowman Modified over 4 years ago

1
**Graph of a Curve Continuity This curve is continuous**

These curves are discontinuous y x y x y x hole gap GAP Smoothness This curve is smooth These curves are not smooth y x y x y x corner cusp

2
**Graph of a Curve (cont’d)**

Increasing Decreasing Constant A function f is increasing on an open interval I if, for any x1 and x2 in I, with x1 < x2, we have f(x1) < f(x2). A function f is decreasing on an open interval I if, for any x1 and x2 in I, with x1 < x2, we have f(x1) > f(x2). A function f is constant on an open interval I if, for any x1 and x2 in I, we have f(x1) = f(x2). x y x1 x2 I f(x1) f(x2) y x x1 x2 I f(x1) f(x2) y x x1 x2 I f(x1) f(x2) Local (or Relative) Extrema f(x1) is a local max and also a global max A function f has a local maximum at x = x0 if locally, f(x0) is greater than all the surrounding values of f(x). We call this f(x0) a local maximum of f. A function f has a local minimum at x = x0 if locally, f(x0) is less than all the surrounding values of f(x). We call this f(x0) a local minimum of f. f(x3) is a local max x1 x2 x3 Global (or Absolute) Extrema A function f has a global maximum at x = x0 if f(x0) is greater than or equal to all values of f(x). We call this f(x0) the global maximum of f. A function f has a global minimum at x = x0 if f(x0) is less than or equal to all values of f(x). We call this f(x0) the global minimum of f. f(x2) is a local min

3
**Use each graph to find the domain and range of the function:**

-5 -4 -3 -2 -1 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 Domain = [–5, –2) (–1, 5] Domain = [–4, 4) Range = (–2, 2] Range = [–3, 1) [2,4) -5 -4 -3 -2 -1 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 Domain = (–∞, –3) [–1, 4) Domain = (–, 5) (5, ) Range = (–, –2) (–1, 3] Range = {–3} [–2, 1) (1, )

4
**1) Find f(5), f(2), and f(–6): f(5) = 3, f(2) = 1, f(–6) = –1 **

Use the graph of the function f given below to answer the following questions: -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 1) Find f(5), f(2), and f(–6): f(5) = 3, f(2) = 1, f(–6) = –1 12) List the interval(s) on which f is decreasing? (–9, –2) (0, 1) (3, 4) 2) Is f(–1) positive? No f(5)? Yes 13) List the interval(s) on which f is increasing? (–2, 0) (1, 3) (4, 5) 3) Is f(2) negative? No f(–4)? Yes 14) List the interval(s) on which f constant? (5, 6) 4) What is the domain of f ? (–9,6] 15) If any, list all the local maxima? 1, 4 At which x values? 0, 3 5) What is the range of f ? [–3,4] 6) What are the x-intercepts? –7.5, –1, 1 16) If any, list all the local minima? –3, 0, 1 At which x values? –2, 1, 4 7) What is the y-intercept? 1 8) Is f continuous? Yes 17) Is there any global maximum? Yes, 4 global minimum? Yes, –3 9) Is f smooth? No 10) For what value(s) of x does f(x) = 0? –7.5, –1, 1 f(x) = 1? 0, 2, 4 11) How often does the line y = 1 intersect the graph? 3 times y = ½? 4 times y = –2? 2 times

Similar presentations

Presentation is loading. Please wait....

OK

Relative Extrema.

Relative Extrema.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google

Ppt on effect of global warming on weather radar Presentations ppt online maker Free ppt on moving coil galvanometer experiment Ppt on earth hour Ppt on eisenmenger syndrome asd Ppt on opposites in hindi Ppt on cross-sectional study designs Ppt on fdi and fii Ppt on maggi product Ppt on review writing