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For the function f(x) = ln(x), find the point where it is not differentiable.

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Question: For the function f(x) = ln(x), find the point where it is not differentiable.

Options:

  1. x = 0
  2. x = 1
  3. x = -1
  4. x = 2

Correct Answer: x = 0

Solution: 

f(x) = ln(x) is not defined for x ≤ 0, hence not differentiable at x = 0.

For the function f(x) = ln(x), find the point where it is not differentiable.

Practice Questions

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

Questions & Step-by-Step Solutions

For the function f(x) = ln(x), find the point where it is not differentiable.
  • Step 1: Understand the function f(x) = ln(x). This is the natural logarithm function.
  • Step 2: Identify the domain of the function. The natural logarithm is only defined for positive values of x, meaning x must be greater than 0.
  • Step 3: Determine where the function is not defined. Since ln(x) is not defined for x ≤ 0, we focus on x = 0.
  • Step 4: Conclude that since f(x) = ln(x) is not defined at x = 0, it cannot be differentiable there.
  • Differentiability – The concept of differentiability relates to whether a function has a defined derivative at a given point.
  • Natural Logarithm Function – The natural logarithm function, ln(x), is only defined for positive values of x.
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