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Determine if the function f(x) = x^3 - 3x + 2 is differentiable at x = 1.

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Question: Determine if the function f(x) = x^3 - 3x + 2 is differentiable at x = 1.

Options:

  1. Yes
  2. No
  3. Only from the left
  4. Only from the right

Correct Answer: Yes

Solution: 

f(x) is a polynomial function, which is differentiable everywhere, including at x = 1.

Determine if the function f(x) = x^3 - 3x + 2 is differentiable at x = 1.

Practice Questions

Q1
Determine if the function f(x) = x^3 - 3x + 2 is differentiable at x = 1.
  1. Yes
  2. No
  3. Only from the left
  4. Only from the right

Questions & Step-by-Step Solutions

Determine if the function f(x) = x^3 - 3x + 2 is differentiable at x = 1.
Correct Answer: Yes, f(x) is differentiable at x = 1.
  • 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.
  • Differentiability of Polynomial Functions – Polynomial functions are continuous and differentiable at all points in their domain.
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