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For the function f(x) = ln(x), find the point where it is not differentiable.
For the function f(x) = ln(x), find the point where it is not differentiable.
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Practice Questions
1 question
Q1
For the function f(x) = ln(x), find the point where it is not differentiable.
x = 0
x = 1
x = -1
x = 2
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f(x) = ln(x) is not defined for x ≤ 0, hence not differentiable at x = 0.
Questions & Step-by-step Solutions
1 item
Q
Q: For the function f(x) = ln(x), find the point where it is not differentiable.
Solution:
f(x) = ln(x) is not defined for x ≤ 0, hence not differentiable at x = 0.
Steps: 4
Show Steps
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.
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