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Let f: Rvec satisfying |f(x)|lt=x^2AAx i...

Let `f: Rvec` satisfying `|f(x)|lt=x^2AAx in R` be differentiable at `x=0.` The find `f^(prime)(0)dot`

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To solve the problem, we need to find the derivative of the function \( f \) at \( x = 0 \), given that \( |f(x)| \leq x^2 \) for all \( x \in \mathbb{R} \) and that \( f \) is differentiable at \( x = 0 \). ### Step-by-step Solution: 1. **Understanding the condition**: We know that \( |f(x)| \leq x^2 \). This implies that as \( x \) approaches \( 0 \), \( f(x) \) must also approach \( 0 \). Specifically, at \( x = 0 \): \[ |f(0)| \leq 0^2 = 0 \implies f(0) = 0. \] ...
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