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Is the function f(x) = x^3 - 3x + 2 differentiable at x = 1?
Is the function f(x) = x^3 - 3x + 2 differentiable at x = 1?
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Practice Questions
1 question
Q1
Is the function f(x) = x^3 - 3x + 2 differentiable at x = 1?
Yes
No
Only left differentiable
Only right differentiable
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The function is a polynomial and hence differentiable everywhere, including at x = 1.
Questions & Step-by-step Solutions
1 item
Q
Q: Is the function f(x) = x^3 - 3x + 2 differentiable at x = 1?
Solution:
The function is a polynomial and hence differentiable everywhere, including at x = 1.
Steps: 5
Show Steps
Step 1: Identify the function given, which is f(x) = x^3 - 3x + 2.
Step 2: Recognize that this function is a polynomial because it is made up of terms with x raised to whole number powers.
Step 3: Understand that polynomials are smooth and continuous functions.
Step 4: Know that all polynomial functions are differentiable everywhere on their domain.
Step 5: Since f(x) is a polynomial, conclude that it is differentiable at x = 1.
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