Скачать или смотреть Locate all absolute maxima and minima for the function f(x,y)=1-2x^2-2y^2| maxima and minima part-1

♥️Maxima and Minima part-2
   • Locate all absolute maxima and minima | Ca...  

In this video, we walk through finding the absolute maximum and minimum of the multivariable function:

f(x, y) = 1 – 2x² – 2y²

✅ We start by computing ∇f = (–4x, –4y) and find the only critical point at (0, 0).
✅ Then we analyze the Hessian matrix, which turns out to be negative definite, confirming a strict local—and in fact, absolute—maximum at (0, 0) with value f(0,0) = 1.
❗ We also explain why there is no absolute minimum (the function decreases without bound as x or y → ±∞).

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Whether you're preparing for AP Calculus BC, JEE, or university-level multivariable calculus, this clear, step-by-step demonstration helps you master critical point tests and Hessian determinants.

💡 **What you’ll learn in this tutorial**:
• How to compute gradients and Hessians for functions of two variables
• How to classify critical points using definiteness
• Why some functions have no absolute minima
• Real-world intuition behind optimization problems

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