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Determine if the function f(x) = x^3 - 3x + 2 is differentiable at x = 1.
Determine if the function f(x) = x^3 - 3x + 2 is differentiable at x = 1.
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Practice Questions
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Q1
Determine if the function f(x) = x^3 - 3x + 2 is differentiable at x = 1.
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f(x) is a polynomial function, which is differentiable everywhere, including at x = 1.
Questions & Step-by-step Solutions
1 item
Q
Q: Determine if the function f(x) = x^3 - 3x + 2 is differentiable at x = 1.
Solution:
f(x) is a polynomial function, which is differentiable everywhere, including at x = 1.
Steps: 4
Show Steps
Step 1: Identify the function given, which is f(x) = x^3 - 3x + 2.
Step 2: Recognize that f(x) is a polynomial function.
Step 3: Understand that polynomial functions are smooth and continuous everywhere.
Step 4: Conclude that since f(x) is a polynomial, it is differentiable at all points, including x = 1.
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