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30. Consider the function defined by 0ifx <0 x if0 < x < 1 = (x)/ 1 if x >1 Sketch this graph and find all points where the graph is continuous but not differentiable.

30. Consider the function defined by 0ifx <0 x if0 < x < 1 = (x)/ 1 if x >1 Sketch this graph and find all points where the graph is continuous but not differentiable.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.6: Regression And Median-fit Lines
Problem 20PFA
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Question 30

y y A H(t) = –16t2 + 40t + 24 0.8 feet. a. Find the velocity of the ball after two seconds. b. When does the ball hit the ground, and what is its impact velocity? 0.4 -1 1 2 x 0.2 c. When does the ball have a velocity of zero? What physical interpretation should be given to this time? -2 -1.0 –0,5 0.5 1.0 25. f(x)= |x – 2| 26. f(x) = 2|x +1| 33. If the data in Figure 2.53 represents a set of measure- ments relating enzyme activity to temperature in degrees Celsius, and the quadratic equation - 27. Let f(x) = &- 3 ifx >1 (-2x if x < 1 A(x) = 11.8 + 19.1 x – 0.2 x² a. Sketch the graph of f. provides a good fit to this data, then find A'(50) and discuss its meaning. b. Show that f is continuous, but not differentiable, at x = : 1. 28. Give an example of a function that is continuous on (-0, 00) but is not differentiable at x = 5. y 29. Consider the function defined by 1 if x < 0 f(x) = -x + 1 1 if x > 0 X +1 10 20 30 40 50 60 Sketch this graph and find all points where the graph is continuous but not differentiable. temperature Figure 2.53 Enzyme activity as a function of temperature. 30. Consider the function defined by (0 i fx <0 x if0 < x <1 34. In Example 7 we discussed how the extent of Arctic sea ice is modeled by the function f(x) = 1 if x > 1 S(t) = 7.292 + 0.023t – 0.004t² million square - kilometers Sketch this graph and find all points where the graph is continuous but not differentiable. where t is years after 1980. Use the definition of the derivative to compute S'(20). How does this value enzyme activity
Transcribed Image Text:y y A H(t) = –16t2 + 40t + 24 0.8 feet. a. Find the velocity of the ball after two seconds. b. When does the ball hit the ground, and what is its impact velocity? 0.4 -1 1 2 x 0.2 c. When does the ball have a velocity of zero? What physical interpretation should be given to this time? -2 -1.0 –0,5 0.5 1.0 25. f(x)= |x – 2| 26. f(x) = 2|x +1| 33. If the data in Figure 2.53 represents a set of measure- ments relating enzyme activity to temperature in degrees Celsius, and the quadratic equation - 27. Let f(x) = &- 3 ifx >1 (-2x if x < 1 A(x) = 11.8 + 19.1 x – 0.2 x² a. Sketch the graph of f. provides a good fit to this data, then find A'(50) and discuss its meaning. b. Show that f is continuous, but not differentiable, at x = : 1. 28. Give an example of a function that is continuous on (-0, 00) but is not differentiable at x = 5. y 29. Consider the function defined by 1 if x < 0 f(x) = -x + 1 1 if x > 0 X +1 10 20 30 40 50 60 Sketch this graph and find all points where the graph is continuous but not differentiable. temperature Figure 2.53 Enzyme activity as a function of temperature. 30. Consider the function defined by (0 i fx <0 x if0 < x <1 34. In Example 7 we discussed how the extent of Arctic sea ice is modeled by the function f(x) = 1 if x > 1 S(t) = 7.292 + 0.023t – 0.004t² million square - kilometers Sketch this graph and find all points where the graph is continuous but not differentiable. where t is years after 1980. Use the definition of the derivative to compute S'(20). How does this value enzyme activity
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