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Determine the points where the function f(x) = x^4 - 4x^3 is not differentiable.
Determine the points where the function f(x) = x^4 - 4x^3 is not differentiable.
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Practice Questions
1 question
Q1
Determine the points where the function f(x) = x^4 - 4x^3 is not differentiable.
x = 0
x = 1
x = 2
None
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The function is a polynomial and is differentiable everywhere. Thus, there are no points where it is not differentiable.
Questions & Step-by-step Solutions
1 item
Q
Q: Determine the points where the function f(x) = x^4 - 4x^3 is not differentiable.
Solution:
The function is a polynomial and is differentiable everywhere. Thus, there are no points where it is not differentiable.
Steps: 5
Show Steps
Step 1: Identify the function given, which is f(x) = x^4 - 4x^3.
Step 2: Recognize that this function is a polynomial.
Step 3: Understand that polynomials are smooth and continuous functions.
Step 4: Recall that polynomials are differentiable everywhere on their domain, which is all real numbers.
Step 5: Conclude that since the function is a polynomial, there are no points where it is not differentiable.
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