(Q2) Consider the graph below of a function f, with a piece missing on the interval (1, 3). Also assume that f extends to -oo and oo along the lines shown. 2 1. 2 4. -1 (a) Suppose that we added a line segment to connect the points (1, 2) and (3, 1) in the given graph. Explain why the resulting function is continuous everywhere. Then find all points where the function is not differentiable. Use definitions appropriately to explain your answers. (b) If the missing piece were such that f was differentiable everywhere instead, show that at some point t in the interval (1,3), the function f has a horizontal tangent line. That is, f'(t) = 0 for some t e (1, 3). (Note: In part (b) you may assume the derivative is 'well-behaved'-that f'(x) is contimuous.)

(Q2) Consider the graph below of a function f, with a piece missing on the interval (1, 3). Also assume that f extends to -oo and oo along the lines shown. 2 1. 2 4. -1 (a) Suppose that we added a line segment to connect the points (1, 2) and (3, 1) in the given graph. Explain why the resulting function is continuous everywhere. Then find all points where the function is not differentiable. Use definitions appropriately to explain your answers. (b) If the missing piece were such that f was differentiable everywhere instead, show that at some point t in the interval (1,3), the function f has a horizontal tangent line. That is, f'(t) = 0 for some t e (1, 3). (Note: In part (b) you may assume the derivative is 'well-behaved'-that f'(x) is contimuous.)

Name: 2.f(z) has a horizontal asymptote: y(Q2) Consider the graph below of
Uploaded: 2024-03-20T06:47:22.000Z
Channel: Bartleby
Description: 2.f(z) has a horizontal asymptote: y(Q2) Consider the graph below of a function f, with a piece missing on the interval (1,3). Also assumethat f extends to -0o and oo along the lines shown.234-1(a) Suppose that we added a line segment to connect the