Problem 2. Prove that the function f : R → R, f (x) = |x|3 is twice differentiable at anypoint a ∈ R, but is not three-times differentiable at 0.

Question

Problem 2. Prove that the function f : R → R, f (x) = |x|3 is twice differentiable at anypoint a ∈ R, but is not three-times differentiable at 0.
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Solution 1

Sure, let's break this down:

Step 1: Define the function and its derivatives

The function is f(x) = |x|^3.

The first derivative of f(x) is f'(x) = 3x|x|.

The second derivative of f(x) is f''(x) = 6|x|.

Step 2: Prove that f(x) is twice differentiable at any point a ∈ R

To prove that f(x) is t Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

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