For the function f(x) = x^3 - 3x^2 + 2, find the points where it is not differen

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Question: For the function f(x) = x^3 - 3x^2 + 2, find the points where it is not differentiable.

Options:

Correct Answer: None

Solution:

As a polynomial, f(x) is differentiable everywhere, hence no points of non-differentiability.

For the function f(x) = x^3 - 3x^2 + 2, find the points where it is not differentiable.

For the function f(x) = x^3 - 3x^2 + 2, find the points where it is not differentiable.

Step 1: Identify the function given, which is f(x) = x^3 - 3x^2 + 2.
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 special type of function. They are made up of terms with variables raised to whole number powers.
Step 4: Know that polynomials are differentiable everywhere on the real number line. This means there are no points where they are not differentiable.
Step 5: Conclude that since f(x) is a polynomial, it is differentiable everywhere, and therefore there are no points of non-differentiability.

Differentiability of Polynomials – Polynomials are continuous and differentiable everywhere on their domain, which is all real numbers.