3.1 Average vs Instantaneous Rate of Change (#limitscontinuity, #differentiation) Consider the piecewise function f(x) = 2x + 5 x ≤-2 sin(x) +1 -2 2 2 1-1/ x 2 (a) Graph f. (b) Find the average rate of change of f from x = -3 to x = 1 and x = 0 to x = 1. Add the corresponding secant lines to your graph. (c) Find the instantaneous rate of change of f at x = 1 and add the corresponding tangent line to your graph. (d) Where is f discontinuous? (e) Where is f not differentiable?
3.1 Average vs Instantaneous Rate of Change (#limitscontinuity, #differentiation) Consider the piecewise function f(x) = 2x + 5 x ≤-2 sin(x) +1 -2 2 2 1-1/ x 2 (a) Graph f. (b) Find the average rate of change of f from x = -3 to x = 1 and x = 0 to x = 1. Add the corresponding secant lines to your graph. (c) Find the instantaneous rate of change of f at x = 1 and add the corresponding tangent line to your graph. (d) Where is f discontinuous? (e) Where is f not differentiable?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 67CR
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![3.1 Average vs Instantaneous Rate of Change (#limitscontinuity, #differentiation)
Consider the piecewise function
f(x) =
2x + 5
x≤-2
sin(x) +1 -2<x<2
x = 2
x > 2
2
1
x
1
2
(a) Graph f.
(b) Find the average rate of change of f from x = −3 to x = 1 and x = 0 to x = 1.
Add the corresponding secant lines to your graph.
(c) Find the instantaneous rate of change of f at x = 1 and add the corresponding
tangent line to your graph.
(d) Where is f discontinuous?
(e) Where is f not differentiable?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5af0e48b-f597-4f3b-a5c6-419ca05c6dd2%2Ff091bed1-ceba-485a-b8f9-ec51dbd6e5c9%2F2ejfcm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3.1 Average vs Instantaneous Rate of Change (#limitscontinuity, #differentiation)
Consider the piecewise function
f(x) =
2x + 5
x≤-2
sin(x) +1 -2<x<2
x = 2
x > 2
2
1
x
1
2
(a) Graph f.
(b) Find the average rate of change of f from x = −3 to x = 1 and x = 0 to x = 1.
Add the corresponding secant lines to your graph.
(c) Find the instantaneous rate of change of f at x = 1 and add the corresponding
tangent line to your graph.
(d) Where is f discontinuous?
(e) Where is f not differentiable?
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