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For the function f(x) = x^2 + 2x + 3, find the point where it is not differentia

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Question: For the function f(x) = x^2 + 2x + 3, find the point where it is not differentiable.

Options:

  1. x = -1
  2. x = 0
  3. x = 1
  4. It is differentiable everywhere

Correct Answer: It is differentiable everywhere

Solution: 

The function is a polynomial and is differentiable everywhere.

For the function f(x) = x^2 + 2x + 3, find the point where it is not differentia

Practice Questions

Q1
For the function f(x) = x^2 + 2x + 3, find the point where it is not differentiable.
  1. x = -1
  2. x = 0
  3. x = 1
  4. It is differentiable everywhere

Questions & Step-by-Step Solutions

For the function f(x) = x^2 + 2x + 3, find the point where it is not differentiable.
  • Step 1: Identify the function given, which is f(x) = x^2 + 2x + 3.
  • Step 2: Recognize that this function is a polynomial.
  • Step 3: Understand that polynomials are smooth and continuous functions.
  • Step 4: Recall that differentiable means the function has a derivative at that point.
  • Step 5: Conclude that since polynomials are differentiable everywhere, there are no points where this function is not differentiable.
  • Differentiability of Polynomials – Polynomials are continuous and differentiable everywhere on their domain, which is all real numbers.
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