Calculus Worksheet 2...Math Calculus Worksheet Chap 2: Differentiation Section: Name: Mr. Lin 3...
1
Math Calculus Worksheet Chap 2: Differentiation Section: Name: Mr. Lin 3 20. Example: Determined the following functions are continuous, differentiable, neither, or both at the point. (a) Continuous ____ Differentiable ____ Neither ____ (b) Continuous ____ Differentiable ____ Neither ____ (c) Continuous ____ Differentiable ____ Neither ____ (d) Continuous ____ Differentiable ____ Neither ____ (e) Continuous ____ Differentiable ____ Neither ____ (f) Continuous ____ Differentiable ____ Neither ____ (g) Continuous ____ Differentiable ____ Neither ____ (h) Continuous ____ Differentiable ____ Neither ____ 21. Example: Given the following graph, at what points does the function appear to be: (a) Continuous but not differentiable— ______________________________________________ (b) Neither continuous nor differentiable— ______________________________________________ 22. Example: Discuss the continuity and differentiability of the function f(x) = |x – 2|. 23. Example: Discuss the continuity and differentiability of the function f(x) = x 1/3 . 24. Example: Find if f(x) is continuous and/or differentiable at x = –1. () = ! + − 3 ≥ −1 − − 4 < −1 . 25. Example: Find if f(x) is continuous and/or differentiable at x = 2. () = ! − 6 + 10 ≥ 2 4 − < 2 . 26. Example: Find the value a and b that make the function f(x) differentiable. () = ! + 1 ≥ 1 − 3 < 1 .
Transcript of Calculus Worksheet 2...Math Calculus Worksheet Chap 2: Differentiation Section: Name: Mr. Lin 3...
Math Calculus Worksheet Chap 2: Differentiation Section: Name:
Mr. Lin
3
20. Example: Determined the following functions are continuous, differentiable, neither, or both at the point.
(a) Continuous ____ Differentiable ____ Neither ____ (b) Continuous ____ Differentiable ____ Neither ____ (c) Continuous ____ Differentiable ____ Neither ____ (d) Continuous ____ Differentiable ____ Neither ____ (e) Continuous ____ Differentiable ____ Neither ____ (f) Continuous ____ Differentiable ____ Neither ____ (g) Continuous ____ Differentiable ____ Neither ____ (h) Continuous ____ Differentiable ____ Neither ____
21. Example: Given the following graph, at what points does
the function appear to be: (a) Continuous but not differentiable—
______________________________________________
(b) Neither continuous nor differentiable—
______________________________________________
22. Example: Discuss the continuity and differentiability of
the function f(x) = |x – 2|.
23. Example: Discuss the continuity and differentiability of the function f(x) = x 1/3.
24. Example: Find if f(x) is continuous and/or differentiable
at x = –1.
𝑓(𝑥) = 𝑥 ! + 𝑥 − 3 𝑥 ≥ −1−𝑥 − 4 𝑥 < −1
.
25. Example: Find if f(x) is continuous and/or differentiable
at x = 2.
𝑓(𝑥) = 𝑥 ! − 6𝑥 + 10 𝑥 ≥ 24 − 𝑥 𝑥 < 2
.
26. Example: Find the value a and b that make the function
f(x) differentiable.
𝑓(𝑥) = 𝑎𝑥 ! + 1 𝑥 ≥ 1𝑏𝑥 − 3 𝑥 < 1
.
