1. Consider the following function, if x # 0 if x = 0 Prove that the function f is differentiable at x = 0 using the definition of {a² sin (²3) derivatives. f(x) = (b) Find the formula of the derivative, f'(x) for x = 0, using any differentiation rules you have learned in this course. Indicate clearly which rules are used in your computation. Note: after this work, you may want to see if the derivative function is continuous at x = 0. While the original function f is differentiable and so also continuous at x = 0, its derivative is not continuous at x = 0.
1. Consider the following function, if x # 0 if x = 0 Prove that the function f is differentiable at x = 0 using the definition of {a² sin (²3) derivatives. f(x) = (b) Find the formula of the derivative, f'(x) for x = 0, using any differentiation rules you have learned in this course. Indicate clearly which rules are used in your computation. Note: after this work, you may want to see if the derivative function is continuous at x = 0. While the original function f is differentiable and so also continuous at x = 0, its derivative is not continuous at x = 0.
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.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 35E
Related questions
Question
100%
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,