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Which of the following statements are true? There can be multiple true statements; indicate all of them. Select 3 correct answer(s) 1). If a function f(x) is differentiable at x=t, it also has to be continuous at x=t. 2). If a function f(x) is continuous at x=t, it also has to be differentiable at x=t. 3). If a function f(x) is not differentiable at x=t, it cannot be continuous at x=t. 4). If a function f(x) is not continuous

Which of the following statements are true? There can be multiple true statements; indicate all of them. Select 3 correct answer(s) 1). If a function f(x) is differentiable at x=t, it also has to be continuous at x=t. 2). If a function f(x) is continuous at x=t, it also has to be differentiable at x=t. 3). If a function f(x) is not differentiable at x=t, it cannot be continuous at x=t. 4). If a function f(x) is not continuous

Calculus For The Life Sciences
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 12CR: Determine whether each of the following statements is true or false and explain why. The derivative...
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Which of the following statements are true? There can be multiple true statements; indicate all of them. Select 3 correct answer(s)

1). If a function f(x) is differentiable at x=t, it also has to be continuous at x=t.

2). If a function f(x) is continuous at x=t, it also has to be differentiable at x=t.

3). If a function f(x) is not differentiable at x=t, it cannot be continuous at x=t.

4). If a function f(x) is not continuous at x=t, it cannot be differentiable at x=t.

5). If a function f(x) is differentiable at x=t, then the limit of f(x) as x→t is equal to f(t).

6). If the limit of f(x) as x→t is equal to f(t), then  f is differentiable at x=t.

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