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Which of the following functions is differentiable everywhere?

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Question: Which of the following functions is differentiable everywhere?

Options:

  1. f(x) =
  2. x
  4. f(x) = x^2
  5. f(x) = sqrt(x)
  6. f(x) = 1/x

Correct Answer: x

Solution: 

f(x) = x^2 is a polynomial and differentiable everywhere.

Which of the following functions is differentiable everywhere?

Practice Questions

Q1
Which of the following functions is differentiable everywhere?
  1. f(x) =
  2. x
  4. f(x) = x^2

Questions & Step-by-Step Solutions

Which of the following functions is differentiable everywhere?
Correct Answer: f(x) = x^2
  • Step 1: Understand what differentiable means. A function is differentiable at a point if it has a defined slope (derivative) at that point.
  • Step 2: Know that polynomials are functions made up of terms like x^n, where n is a non-negative integer.
  • Step 3: Recognize that polynomials, like f(x) = x^2, are smooth and continuous everywhere on the graph.
  • Step 4: Conclude that since f(x) = x^2 is a polynomial, it is differentiable at every point on the graph.
No concepts available.
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