Mechanical Engineering > Gate 2024 > Differential Equation
Let f(⋅) be a twice differentiable function from ℝ² → ℝ.
If p, x0 ∈ ℝ² where ‖ p ‖ is sufficiently small
(here ‖ ⋅ ‖ is the Euclidean norm or distance function), then:
f(x0 + p) = f(x0) + ∇f(x0)T p + (1/2) pT ∇² f(ψ) p
where ψ ∈ ℝ² is a point on the line segment joining x0 and x0 + p. If x0 is a strict local minimum of f(x), then which one of the following statements is TRUE?
f(x0 + p) = f(x0) + ∇f(x0)T p + (1/2) pT ∇² f(ψ) p
where ψ ∈ ℝ² is a point on the line segment joining x0 and x0 + p. If x0 is a strict local minimum of f(x), then which one of the following statements is TRUE?
Correct : a
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