Question: For the function f(x) = x^3 - 3x^2 + 4, find the value of x where f is not differentiable.
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Correct Answer: 0
Solution:
The function is a polynomial and is differentiable everywhere, so there is no such x.
For the function f(x) = x^3 - 3x^2 + 4, find the value of x where f is not diffe
Practice Questions
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For the function f(x) = x^3 - 3x^2 + 4, find the value of x where f is not differentiable.
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Questions & Step-by-Step Solutions
For the function f(x) = x^3 - 3x^2 + 4, find the value of x where f is not differentiable.
Step 1: Identify the function given, which is f(x) = x^3 - 3x^2 + 4.
Step 2: Understand what it means for a function to be differentiable. A function is differentiable at a point if it has a defined derivative at that point.
Step 3: Recognize that polynomials are a type of function that are smooth and continuous everywhere.
Step 4: Since f(x) is a polynomial, it does not have any points where it is not differentiable.
Step 5: Conclude that there is no value of x where f is not differentiable.
Differentiability of Polynomials – Polynomials are continuous and differentiable everywhere on their domain, which is all real numbers.
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